Question

According to data released in​ 2016, 69​% of students in the United States enroll in college directly after high school graduation. Suppose a sample of 232 recent high school graduates is randomly selected. After verifying the conditions for the Central Limit Theorem are​ met, find the probability that at most 66​% enrolled in college directly after high school graduation.

Answer 1

Answer:

15.87%

Step-by-step explanation:

The Random and Independent condition holds assuming independent.

The Large Samples condition Holds

The Big Populations condition can reasonably be assumed to hold.

Hence,

P(Atmost 66%)

$P(z<\frac{0.66-0.69}{\sqrt{0.69\times0.31/242} })$

= P(z < -1.0090)

= 0.1587

= 15.87%

Answer 2

The probability that at most 66​% enrolled in college directly after high school graduation is; 0.162

How to use the central limit theorem?

We are given;

Population mean; μ = 69% = 0.69

Sample size; n = 232

Thus;

Population standard deviation is;

σ = √(μ(1 - μ)/n)

σ = √(0.69(1 - 0.69)/232)

σ = 0.0304

z-score is gotten from;

z = -0.9868

From online p-value from z-score calculator, we have;

p-value = 0.162

z = (0.66 - 0.69)/0.0304

z = -0.9868

From online p-value from z-score calculator, we have;

p-value = 0.162

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