Question

The National Center for Education Statistics reports that the proportion of college freshmen who return to the same school for their sophomore year is 0.69. Suppose we select a random sample of 480 freshmen from across the nation.

Question 1. What is the expected value of the sampling distribution model for the proportion of 480 freshmen that will return to the same school for their sophomore year?

Question 2. What is the standard deviation of the sampling distribution model for the proportion of 480 freshmen that will return to the same school for their sophomore year? (Round to 3 decimal places)

Question 3. What is the probability that the proportion of these 480 freshmen that return to the same school for their sophomore year is less than 0.75? (Round to 4 decimal places)

Answer 1

Solution

Given that,

p = 0.69

1 - p = 1 - 0.69 = 0.31

n = 480

1)   = p = 0.69

2) =  [p ( 1 - p ) / n] =   [(0.69 * 0.31) / 480 ] = 0.021

3) P( < 0.75 )

= P[( - ) / < (0.75 - 0.69) / 0.021]

= P(z < 2.86)

Using z table,

= 0.9979