Question

A small liberal arts college in the Northeast has 150 freshmen. Forty of the freshmen are education majors. Suppose fifteen freshmen are randomly selected (without replacement).

Find the expected number of education majors in the sample. Round your answer to two decimal places, if necessary.

Answer 1

The expected number of education majors in a sample of fifteen freshmen from the college is 4.00 when rounded to two decimal places.

Step-by-step explanation:

To find the expected number of education majors in a sample of fifteen freshmen randomly selected without replacement from a liberal arts college with 150 freshmen, where forty of the freshmen are education majors, we use the concept of expectation in probability.

The expectation (E) of the number of education majors in the sample is given by:

E = (Number of successes in population / Total population) × Sample size
E = (40/150) × 15

Calculating this:

E = (0.2667) × 15
E = 4.00

Therefore, we would expect there to be an average of 4 education majors in a sample of 15 randomly selected freshmen from this college.