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AP® Statistics

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Robbie's Red Cards

APSTAT-4XKLKB

A standard deck of playing cards is made up of $26$ red cards and $26$ black cards. Robbie shuffles and deals a card and records its color. She replaces the card in the deck and repeats this process $25$ times, obtaining $10$ red cards and $15$ black cards - only $40\%$ red!

Does Robbie have reason to believe the deck of cards has an unusually small proportion of red cards?

Calculate the probability of obtaining a sample proportion less than or equal to $0.4$.

A

$0.16$

B

$0.26$

C

$0.74$

D

$0.84$

E

The conditions for using the normal model are not met in this situation.