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In a large metropolitan area, the proportion of high school seniors who drive to school at least $3\text{ days a week}$ is $0.45$. A random sample of $25\text{ students}$ is chosen.

How would you calculate the probability that at least $13$ of these students drive to school at least $3\text{ days a week}$?

A

Use the multiplication rule for probabilities for the following item from the sample space, where D = drives and N = does not drive:

(DDDDDDDDDDDDDNNNNNNNNNNNN)

B

Calculate the binomial probability on a calculator using $\mu = 11.25$, $\sigma = 6.19$, and $X \ge 13$.

C

Use the normal approximation to the binomial because the sample size is large.

D

Use the binomial formula for $n = 25$, $X = 13$, and $p = 0.45$.

E

Use the normal approximation to the binomial because $np \ge 10$ and $n(1-p) \ge 10$.

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