Question

A national college researcher reported that 67%of students who graduated from high school in 2012 enrolled in college. Twenty-nine high school graduates are sampled What is the mean number who enroll in college in a sample of 29 high school graduates? Round the answer to two decimal places. a) What is the standard deviation of the number who enroll in college in a sample of 29 high school graduates? Round the answer to four decimal places.

Answer 1

Answer:

Mean is 19.43

Standard deviation is 2.5322

Step-by-step explanation:

For each student who graduated from high school in 2012, there are only two possible outcomes. Either they have enrolled in college, or they have not. The probability of a student having enrolled in college is independent of other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

67% of students who graduated from high school in 2012 enrolled in college.

This means that $p = 0.67$

Sample of 29 high school graduates

This means that $n = 29$

Mean

$E(X) = np = 29*0.67 = 19.43$

Standard deviation

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{29*0.67*0.33} = 2.5322$