# Exam P Practice Problem 106 – average height of students

Problem 106-A

Heights of male students in a large university follow a normal distribution with mean 69 inches and standard deviation 2.8 inches.

Four male students from this university are randomly selected.

Determine the probability that the average height of the selected students is between 5 feet 7 inches and 5 feet 11 inches.

Note that one feet = 12 inches.

$\displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 1 \bold 1 \bold 0 \bold 4$

$\displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 5 \bold 2 \bold 2 \bold 2$

$\displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 8 \bold 4 \bold 7 \bold 2$

$\displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 8 \bold 8 \bold 9 \bold 6$

$\displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 9 \bold 0 \bold 7 \bold 5$

The answers are based on this normal table from SOA.

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Problem 106-B

Heights of female students in a large university follow a normal distribution with mean 65 inches and standard deviation 2.2 inches.

Sixteen female students are randomly selected.

Determine the probability that the average height of the selected students is greater than 5 feet 6 inches.

Note that one feet = 12 inches.

$\displaystyle \bold ( \bold A \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 0 \bold 3 \bold 4 \bold 4$

$\displaystyle \bold ( \bold B \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 1 \bold 7 \bold 8 \bold 2$

$\displaystyle \bold ( \bold C \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 3 \bold 2 \bold 6 \bold 4$

$\displaystyle \bold ( \bold D \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 4 \bold 5 \bold 7 \bold 2$

$\displaystyle \bold ( \bold E \bold ) \ \ \ \ \ \ \ \ \ \ \ \ \bold 0 \bold . \bold 6 \bold 7 \bold 3 \bold 6$

The answers are based on this normal table from SOA.

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