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AP® Statistics

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Definition: Conditions

APSTAT-Y1EPRX

Suppose a middle school gym currently has $50$ students inside: $28$ students are in $7$th grade, and $22$ students are in $8$th grade. The principal decides to randomly select $5$ of these students to represent the school at the school board meeting.

Four of the $5$ students randomly chosen happened to be in the $8$th grade. The principal’s secretary, surprised by this result, uses binomial calculations to find the likelihood of $4$ or more of those $5$ selected students being in the $8$th grade.

Why would it be incorrect to use binomial calculations in this situation?​

A

The probability of a $7$th grader versus an 8th grader is not $50\%$.

B

There is not a fixed number of trials.

C

The selections are not independent.

D

There are not two outcomes (success/failure).

E

The sample size is too small to use binomial calculations.