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Standard 52-card deck

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Standard 52-card deck

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Cards from a standard 52-card deck

The standard 52-card deck of French-suited playing cards is the most common pack of playing cards used today.[a] In English-speaking countries it is the only traditional pack[b] used for playing cards; in many countries of the world, however, it is used alongside other traditional, often older, standard packs with different suit symbols and pack sizes. The most common pattern worldwide and the only pattern commonly available in Britain and America is the English pattern pack. The second most common is the Belgian-Genoese pattern, designed in France, but whose use spread to Spain, Italy, the Ottoman Empire, the Balkans and much of North Africa and the Middle East.[1] In addition to those, there are other major international and regional patterns.

Composition

A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠), with reversible (double-headed) court cards (face cards). Each suit includes an Ace, a King, Queen and Jack, each depicted alongside a symbol of its suit; and numerals or pip cards from the Deuce (Two) to the Ten, with each card depicting that many symbols (pips) of its suit. Anywhere from one to six (most often two or three since the mid-20th century) Jokers, often distinguishable with one being more colourful than the other, are added to commercial decks, as some card games require these extra cards.[2][3]

Example set of 52 playing cards; 13 of each suit: clubs, diamonds, hearts, and spades

Ace

2

3

4

5

6

7

8

9

10

Jack

Queen

King
Clubs

Diamonds

Hearts

Spades

Design

Dondorf Rhineland pattern

The most popular standard pattern of the French deck is the English pattern[c] (pictured below), sometimes referred to as the International pattern or Anglo-American pattern.[4] The second most common is the Belgian-Genoese pattern, which was designed in France for export and spread to Spain, Italy, the Ottoman Empire, the Balkans and much of North Africa and the Middle East.[1] There are also numerous others such as the Berlin pattern, Nordic pattern, Dondorf Rhineland pattern (pictured right) and the variants of the European pattern.

Modern playing cards carry index labels on opposite corners or in all four corners to facilitate identifying the cards when they overlap and so that they appear identical for players on opposite sides. For the court cards, this comprises the initial letter or letters from the name of that card. In English countries they are lettered A, K, Q and J for Ace, King, Queen and Jack. In other countries the letters may vary. Germany uses A, K, D and B (As, König, Dame and Bube); Russia uses T, K, D and B (Tuz, Korol, Dama and Valet); Sweden uses E, K, D and Kn (Ess, Kung, Dam and Knekt) and France uses 1, R, D, V (1, Roi, Dame, and Valet).

Although French-suited, 52-card packs are the most common playing cards used internationally, there are many countries or regions where the traditional pack size is only 36 (Russia, Bavaria) or 32 (north and central Germany, Austria) or where regional cards with smaller packs are preferred for many games. For example, 40- or 48-card Italian-suited packs are common in Italy; 40- and 48-card Spanish-suited packs on the Iberian peninsula; and 36-card German-suited packs are very common in Bavaria and Austria. In addition, tarot cards are required for games such as French tarot (78 cards), which is widely played in France, and the Tarock family of games (42 or 54 cards) played in countries like Austria and Hungary.

History

English pattern

The English pattern pack originated in Britain which was importing French playing cards from Rouen and Antwerp by 1480. The earliest cards of the English pattern date to around 1516. But Britain only started manufacturing its own cards towards the end of the 16th century, when card production began in London. These were based on the Rouen pattern, but unlike the traditional French cards, they dropped the names on the court cards. The English pattern evolved, in the process losing “some of its Rouen flavour and elegance and became more and more stylised. The figures took more space in the cards and many details were distorted.”[4]

All early cards of this type were single-headed, but around 1860, the double-headed cards, universally used on modern decks, appeared. Corner indices were added around 1880. During the 19th century, the English pattern spread all over the world and is now used almost everywhere, even in countries where traditional patterns and other suits are popular. In America, the English pattern was copied onto wider cards.[4]

The fanciful design and manufacturer’s logo commonly displayed on the ace of spades began under the reign of James I of England, who passed a law requiring an insignia on that card as proof of payment of a tax on local manufacture of cards. Until August 4, 1960, decks of playing cards printed and sold in the United Kingdom were liable for taxable duty and the ace of spades carried an indication of the name of the printer and the fact that taxation had been paid on the cards.[d] The packs were also sealed with a government duty wrapper.

Size of the cards

Manufacturer

Country

Marketed for

Length

Width
in

mm

in

mm
Ravensburger

Germany

Poker

3.6

92

2.3

59
Handa (wide)[e]
Denmark

not specified

3.6

91

2.4

62
ASS Altenburger

Germany

Poker, Rummy

3.6

91

2.3

59
Kem (wide)

US

Poker[f]
3.5

89

2.5

64
Piatnik (narrow)

Austria

Bridge, Poker, Whist

3.5

89

2.3

58
Kem (narrow)

US

Bridge

3.5

89

2.25

57
Piatnik (wide)

Austria

Classic Poker, Poker Pro

3.5

88

2.5

63
Waddingtons

UK

not specified

3.5

88

2.3

58
Handa (narrow)

Denmark

not specified

3.4

87

2.2

56
Oberg

Sweden

Poker

3.4

87

2.2

56
Bicycle

US

Poker

3.5

88

2.5

63

Standard playing cards are available in various sizes, sometimes designated as “wide” and “narrow” or referred by the manufacturer as either “poker” or “bridge” sized;[5] nominal dimensions are summarized in the adjacent table. However, there is no formal requirement for precise adherence and minor variations are produced by various manufacturers in different countries.[6] In Germany, for example, standard Poker and Rummy packs by ASS Altenburger and Ravensburger measure 92 × 59 mm.[7] Austria’s Piatnik sells packs marketed for Bridge, Poker and Whist measuring 89 × 58 mm;[8] while Britain’s Waddingtons produce generic packs sized at 88 × 58 mm.

The slightly narrower cards are more suitable for games such as bridge and some types of poker, where a number of cards must be held or concealed in a player’s hand. In most U.S. casino poker games, plastic bridge (narrow) sized cards are used; this is for both ease of use and dealing, and the plastic cards last much longer than paper decks. U.S. casino shuffling machines have traditionally been designed for bridge-size (narrow) cards for these reasons. In other table games, such as 21 (blackjack), a modern casino may use hundreds or even thousands of decks per day, so paper cards are used for those, for economic reasons. Poker-size (wide) paper decks are used for 21 and other similar games. Other sizes are also available, such as a smaller ‘patience’ size (usually 1 3⁄4 × 2 3⁄8 in or 44 × 60 mm) and larger ‘jumbo’ ones for card tricks.

The thickness and weight of modern playing cards are subject to numerous variables related to their purpose of use and associated material design for durability, stiffness, texture and appearance.[9]

Markings

Some decks include additional design elements. Casino blackjack decks may include markings intended for a machine to check the ranks of cards, or shifts in rank location to allow a manual check via an inlaid mirror. Many casino decks and solitaire decks have four indices instead of just two. Some modern decks have bar code markings on the edge of the face to enable them to be sorted by machine (for playing duplicate bridge, especially simultaneous events where the same hands may be played at many different venues). Some decks have large indices for clarity. These are sometimes sold as ‘seniors’ cards’ for older people with limited eyesight, but may also be used in games like stud poker, where being able to read cards from a distance is a benefit and hand sizes are small.

Four-colour packs

Main article: Four-colour pack

The standard French-suited pack uses black for the spades and clubs, and red for the hearts and diamonds. However, some packs use four colours for the suits in order to make it easier to tell them apart. There are several schemes: a common one is the English Poker format with black spades (♠), red hearts (♥), blue diamonds (♦) and green clubs (♣). Another common system is based on the German suits and uses green spades (♠) and yellow diamonds (♦) with red hearts (♥) and black clubs (♣).

Nomenclature

When giving the full written name of a specific card, the rank is given first followed by the suit, e.g., “ace of spades” or “Ace of Spades”.[g] Shorthand notation may reflect this by listing the rank first, “A♠”; this is common usage when discussing poker; but it is equally common in more general sources to find the suit listed first, as in “♠K” for a single card or “♠AKQ” for multiple cards. This common practice when writing about bridge as it helps differentiate between the card(s) and the contract (e.g. “4♥”, a contract of four hearts). Tens may be either abbreviated to T or written as 10.

Terminology

Common collective and individual terms for playing cards relevant, but not exclusive to, the 52-card pack are:

Face cards or court cards – jacks, queens and kings.
Honour cards – aces and the face cards
Wild cards – When deciding which cards are to be made wild in some games, the phrase “acey, deucey or one-eyed jack” (or “deuces, aces, one-eyed faces”) is sometimes used, which means that aces, twos, and the one-eyed jacks are all wild.
Numerals or pip cards are the cards numbered from 2 to 10.
“2” cards are also known as deuces.
“3” cards are also known as treys.
“4” cards are also known as sailboats
“8” cards are also known as snowmen

Nicknames

For a comprehensive list of card nicknames, see List of playing-card nicknames.
One-eyed Royals – the jack of spades and jack of hearts (often called the “one-eyed jacks”[10]) and the king of diamonds are drawn in profile; therefore, these cards are commonly referred to as “one-eyed”. The rest of the courts are shown in full or oblique face.
The jack of diamonds is sometimes known as “laughing boy”.[10]
Suicide kings – The king of hearts is typically shown with a sword behind his head, making him appear to be stabbing himself. Similarly, the one-eyed king of diamonds is typically shown with an ax behind his head with the blade facing toward him. These depictions, and their blood-red colour, inspired the nickname “suicide kings”.[10]
The king of diamonds is traditionally armed with an ax, while the other three kings are armed with swords; thus, the king of diamonds is sometimes referred to as “the man with the axe”. This is the basis of the trump “one-eyed jacks and the man with the axe”. Poker may be played with wild cards, often “Aces, Jacks, and the King with the Axe”.[10]
The ace of spades, unique in its large, ornate spade, is sometimes said to be the death card or the picture card, and in some games is used as a trump card.[10]
The queen of spades usually holds a sceptre and is sometimes known as “the bedpost queen”, though more often she is called the “black lady”. She also is the only queen facing left.[10]
In many decks, the queen of clubs holds a flower. She is thus known as the “flower queen”, though this design element is among the most variable; the Bicycle Poker deck depicts all queens with a flower styled according to their suit.[10]

Combinations

It has been shown that because of the large number of possibilities from shuffling a 52-card deck (52!, equaling roughly 8.0658×1067 or 80,658 vigintillion possibilities), it is probable that no two fair card shuffles have ever yielded exactly the same order of cards.[11]

Unicode

As of Unicode 7.0, playing cards are now represented. Note that the following chart (“Cards”, Range: 1F0A0–1F0FF) includes cards from the Tarot Nouveau deck, as well as the standard 52-card deck.

Playing Cards[1][2]Official Unicode Consortium code chart (PDF)
 
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
U+1F0Ax

🂠

🂡

🂢

🂣

🂤

🂥

🂦

🂧

🂨

🂩

🂪

🂫

🂬

🂭

🂮

U+1F0Bx

🂱

🂲

🂳

🂴

🂵

🂶

🂷

🂸

🂹

🂺

🂻

🂼

🂽

🂾

🂿
U+1F0Cx

🃁

🃂

🃃

🃄

🃅

🃆

🃇

🃈

🃉

🃊

🃋

🃌

🃍

🃎

🃏
U+1F0Dx

🃑

🃒

🃓

🃔

🃕

🃖

🃗

🃘

🃙

🃚

🃛

🃜

🃝

🃞

🃟
U+1F0Ex

🃠

🃡

🃢

🃣

🃤

🃥

🃦

🃧

🃨

🃩

🃪

🃫

🃬

🃭

🃮

🃯
U+1F0Fx

🃰

🃱

🃲

🃳

🃴

🃵

Notes
1.^ As of Unicode version 13.0
2.^ Grey areas indicate non-assigned code points

See also

500 decks come with extra ranks.
French playing cards
German playing cards
Italian playing cards
Spanish playing cards
Stripped decks come with fewer ranks.
Tarot Nouveau, the most common French-suited tarot game deck

Notes

^ 52 cards excluding any Jokers.

^ ‘Deck’ and ‘pack’ are synonymous; ‘deck’ tends to be used in America and ‘pack’ elsewhere.

^ ‘English pattern’ is the name recommended by the IPCS.

^ The Stamp Act 1765 imposed a tax on playing cards.

^ Taken from a pack with a tourist motif, so may have been aimed at American market.

^ Kem Poker cards are close to the B8 (88 x 62 mm) size of ISO 216.

^ Sources vary as to the capitalisation used with American sources tending to favour lower case and British sources tending towards capitals, but there are numerous exceptions and some sources combine them e.g “Ace of spades”.

References

^ a b Pattern Sheet 80 at i-p-c-s.org. Retrieved 23 August 2020.

^ McLeod, John. Games played with French suited cards at pagat.com. Retrieved 17 April 2017.

^ French regional pattern sheets and French non-regional pattern sheets at i-p-c-s.org. Retrieved 17 April 2017.

^ a b c .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:”\”””\”””‘””‘”}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg”)right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url(“//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg”)right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}”The English pattern”. International Playing-Card Society. Retrieved 17 April 2017.

^ Kem Cards official website. Narrow (Bridge) Size verses Wide (Poker) Size, retrieved 2014-02-27.

^ In a sample of 95 American bridge and poker card sets, lengths ranged from 87.50 mm to 89.50 mm. In a sample of 28 bridge sized cards, widths varied from 56.98 mm to 58.25 mm. In a sample of 67 poker sized cards, widths varied from 62.44 to 63.54 mm. Reference: Home Poker Tourney website. Playing Card Review, retrieved 2014-02-27.

^ Poker at ravensburger.de. Retrieved 21 August 2020.

^ Bridge – Poker – Whist at piatnik.com. Retrieved 21 August 2020.

^ In a sample of 28 bridge-sized cards, the weight of a card varied from 1.8 g to 2.48 g and thickness from 0.26  mm to 0.34  mm. In a sample of 67 poker-sized cards, the weight of a card varied from 1.4 g to 2.78 g and thickness from 0.24 mm to 0.34 mm. Reference: Home Poker Tourney Web site. Playing Card Review, retrieved 2014-02-27.

^ a b c d e f g Common Playing Card Nicknames at playingcarddecks.com. Retrieved 10 November 2020.

^ “The Amazing Truth About a Deck of Cards”. KnowledgeNuts.

vtePlaying cardsStandard52-card pack
Suit/rank

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2
Spades ♠

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2
Hearts ♥

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2
Diamonds ♦

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2
Clubs ♣

Ace

King

Queen

Jack

10

9

8

7

6

5

4

3

2
Other packs
Piquet pack
French pack
German pack
Italian pack
Spanish pack
Swiss pack
Tarot pack
Four-colour packOther cards
Banner
Blank
Face card/Court card (Knight, Ober, Unter)
Pip card (Deuce, Weli)
Joker
Card nicknames
Stripped deck
Talon
UnicodeOther suits
German: Acorns
Leaves
Hearts
Bells
Swiss: Acorns
Shields
Roses
Bells
Latin (Italian/Spanish): Cups
Coins
Batons
Swords
vtePlaying card decksItalicized are not used for games at presentBy suit-systemFrench
Standard 52-card deck
500
Four-color deck
Russian
Adler-Cego
Industrie und Glück
Tarot NouveauGerman
German
Northern
Southern
Württemberg
William Tell
SwissLatin
Italian
Tarocco Bolognese
Tarocco Piemontese
Swiss 1JJ
Tarot of Marseilles
Tarot de Besançon
Trappola
Spanish
Aluette
Portuguese
Tarocco Siciliano
MinchiateSingle-suited
As-Nas
Gnav
KvitlechBy geography
Chinese
Zi pai
Chess-suited: Four Color Cards, Tam cúc
Money-suited: Madiao, Tổ tôm
Ganjifa
Dashabatar Cards
Ganjapa
Karuta
Hanafuda
Kabufuda
Uta-garuta
Tujeon
vteNon trick-taking card games
Shuffling
Cutting
Glossary of card game termsAdding
Cribbage
Costly Colours
Ninety-nine
NoddyCollecting
Beggar-my-neighbour
Egyptian Ratscrew
My Ship Sails
Ninety-nine
Ochse, leg dich!
Quartets
Schlafmütze
WarCommerce
Brag
Commerce
James Bond
Kemps
Schwimmen
Stop the BusCompendium
Barbu
Bauernfangen
Bonken
Dreeg
Herzeln
Kein Stich
King
Lorum
Poch
Quodlibet
Rosbiratschka
TrexDraw and discard
Buraco
Colonel
Canasta
Carioca
Continental Rummy
Contract Rummy
German Rummy
Golf
Kalooki
Militaire
Robbers’ rummy
Rummy
Gin rummy
Rumino
Thirty-one
Three Thirteen
Tonk
Treppenrommé
Viennese Rummy
Yaniv
500 RumFishing
Bastra
Byggkasino
Cassino
Cicera
Cuarenta
Escoba
Pasur
Go-Stop
Mulle
Scopa
Skwitz
Tablanette
ZwickerMatching
Kings in the Corner
Lusti-Kartl’n
Nain Jaune
Newmarket
Poch
Ristikontra
Sedma
Sedmice
Snip-Snap-SnorumShedding
Bartok
Big two
Craits
Crazy Eights
Cheat
Daifugō
Dou dizhu
Dupa biskupa
Durak
Hund
Irish switch
Jack Change It
Kille
Last Card
Mao
Mau-Mau
One-card
Paskahousu
President
Ranter-Go-Round
Quatorze
Ristiseiska
Shithead
Spit
Switch
{{Historical card games}} {{Trick-taking card games}} {{Tarot and Tarock card games}}

Retrieved from “https://en.wikipedia.org/w/index.php?title=Standard_52-card_deck&oldid=1017407023”

A standard deck of cards contains 52 cards. One card is selected...

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Probability of 5 Card Hands Using Combinations: Part 1 – Five cards are drawn randomly from a standard deck of 52 cards.
We're asked to give each
probability as a percentage to four decimal places, which means we'll first
find the probability to six decimal places and
then convert to a percentage. We're first asked to find the probability that exactly three cards are kings. We need to be careful here, because if exactly three cards are kings, then we also have two
cards that are not kings, because we are drawing five cards. The probability of an event is equal to the favorable number of outcomes divided by the total number of outcomes. Let's beginning by
determining the total number of possible outcomes
when drawing five cards from a deck of 52 cards. Because the order does not matter, the number of ways of selecting five cards from 52 cards is 52 choose five. Again we use a combination because the order does not matter. And now the favorable number of outcomes is going to be the number of ways we can select three kings from the kings in the deck and then times the number of ways we can select two cards that
are not kings from the deck. And there are four kings in a deck and therefore the number
of ways of selecting three kings from four
kings is four choose three and then we have times the number of ways we can select two cards from
the deck that are not kings. Well if there are four kings in the deck, then there must be 52 minus four or 48 cards that are not kings. And therefore the number
ways of selecting two cards that are not kings is 48 choose two. So the number of favorable outcomes is equal to four choose
three times 48 choose two. And let's evaluate this on the calculator. And again we'll have to get the decimal to six decimal places so the percentage is accurate
to four decimal places. We need the numerator in parentheses, so we have open parenthesis
four choose three, right arrow times 48 choose two, right arrow, closed parenthesis, and this is divided by, in
parentheses, 52 choose five, which to six decimal places
is approximately 0.001736. Which as a percentage is 0.17336%. Next we're asked to find the probability that all five cards are hearts. And again the total number of outcomes is going to be 52 choose five. The favorable number of outcomes is equal to the number of
ways we can select five hearts from the hearts in the deck and since there are 13 hearts in the deck, the number of ways of selecting
five hearts from 13 hearts is 13 choose five. And this does accommodate for
all five cards being drawn and therefore this quotient
is the probability. So going back to the calculator we have 13 choose five, divided by 52 choose five. Notice how this is giving
us scientific notation. This means 4.95 et cetera times 10 raised to the power of negative four. To convert to a decimal, we move the decimal point
four places to the left which'll give us 0.000495
to six decimal places. Which is equal to 0.0495%. Again, the calculator gave us approximately 4.95 times
10 to the negative four which is equal to 0.000495. Notice how to go from scientific notation to decimal notation you
move the decimal point four places to the left, because the exponent was negative four. For the last example we'll
asked to find the probability that exactly four cards are face cards, which means four cards will be face cards and one card will not be a face card. The total number of possible outcomes is still going to be 52 choose five. And now for the favorable outcomes, let's first determine how many ways we can select four face cards from the 12 face cards in the deck. Because there are 12
face cards in the deck, the number of ways of
selecting four face cards is 12 choose four. We have to multiply this by the number of ways of selecting one card that is not a face card. And the number of cards
that are not face cards is equal to 52 minus 12 of 40. And therefore the number of ways of selecting one card
that is not a face card is 40 choose one. And now let's go back to the calculator. So in parentheses, we have 12 choose four times 40 choose one divided by 52 choose five. And now see this isn't correct because I forgot to divide here, so I'll press second enter to bring up these previous entry. Move the cursor to here and press
second, delete for insert and then divide and then press enter. So to six decimal places we
have approximately 0.007618, which as a percentage is 0.7618%. I hope you found this helpful. .

Four cards are drawn at random from a pack of 52 cards – .

HW – 5.2 – 04 – We're looking at homework for section 5.2.
This is question #4. It's a multipart question. In a survey of a group of men, the Heights in the 20 to 29 age group were normally distributed with a mean of 68.7 inches in a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts A through D below. So we'll start with part A. Find the probability that a study participant has a height that is less than 67 inches. So we have to find our Z score for X equals 67. The Z score formula is Z equals X minus mu over Sigma. So in this context it would be 67 – 68.7 over 4. 67 – 68.7 is -1.7 over 4. Which ends up being -.425 we're going to round to two decimal places because the Z scores in our standard normal distribution table are two decimal place Z scores, so this would round to-0.43. Since that's a negative Z score, we're going to need the negative side of the standard normal distribution table. We look up Z equals -.43 and we find our table value which ends up being our area of .3336. So the probability that X is less than 67 is going to be .3336. So that's your answer for part A. For Part B. Find the probability that a study participant has a height that is between 67 and 70 inches. So we already found the Z score that was associated with the X equals 67. So let's go ahead and find the Z score for X equals 70. When X equals 70, we use X minus mu over Sigma, so that's going to be 70 – 68.7 over 4. Which is 1.3 over 4. Which is .325 rounded to two decimal places is 0.33. So that means we need the positive side of the standard normal distribution table. So our table value here is going to be .6293. And then our probability. We can use the value from part A along with this value we just found for X equals 70. And it's going to be .6293 minus the .3336. From part A, because we always do the table value that's furthest right minus the table value on the left. And when we do the subtraction, we end up with .2957. And that is your answer for Part B. For part C. We're looking to find the probability that a study participant has a height that is more than 70 inches. So we've already computed the Z score for X equals 70. It was Z equals .33. So because this is a greater than area. A greater than probability. Then we do 1 minus the table value for that Z score. And we get. 1 – .6293. Which gives us an area of .3707 and that area is equal to the probability. So the probability that X is greater than 70 is .3707 Now we're ready to answer Part D. Identify any unusual events. Well, remember an unusual event would be an event that had a probability that was less than .05. So when you look back at parts A, B & C, none of those were less than .05, so there are no unusual events. And that's your answer. .