Question

W e will not be enough college graduates? 23) Favorite Cookie e Hilly two percent of adults say chocolate chip is their Fifty-two percent of adults say Orte. You randomly select 40 adults and ask each if chocolate chip is his or her favorite cookie. (Source: Wearever) Find the probability that at most 23 people say chocolate chip is the favorite cookie. (h) Find the

Answer 1

This is a binomial distribution question with
n = 40
p = 0.52
q = 1 - p = 0.48
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that
$\\Mean (\mu) = np = 40 * 0.52 = 20.8 \\Standard\; deviation (\sigma) = \sqrt{npq} = \sqrt{40*0.52*0.48} = 3.1597 \\Also \\z_{ score } = \frac{x-\mu}{\sigma}$

a)
$\\P(x \le 23.0)=? \\P(x \le 23.0) = P(x < 23.5)\;\;\;\; (By\;Continuity\;Correction)$
The z-score at x = 23.5 is,
$\\z = \frac{23.5-20.8}{3.1597}$
z = 0.8545
This implies that
$\\P(x \le 23.0) = P(x < 23.5) = P(z < 0.8545) = \textbf{0.8036}$
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