Question

Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches. If 500 men want to enlist in the U.S. Marine Corps, how many would you not expect to meet the height requirements?

A. 19
B. 19%
C. 481
D. 154

Answer 1

a. 19

Explanation:

We have a normal distribution with parameters
`\mu=69.0` and
`\sigma=2.8`.

If the limits that requires the U.S Maine Corps is a height between 64 and 78 inches, we can express the proportion of rejected as:

`P(rejected)=P(x<64.0)+P(x>78.0)`

We can calculate the z-values to calculate this probabilities by table.

`z_1=(x_1-\mu)/(\sigma)=(64.0-69.0)/(2.8)=  -1.786\\\\z_2=(x_2-\mu)/(\sigma)=(78.0-69.0)/(2.8)=3.214`

Then we can express the probability as

`P(rejected)=P(z<-1.786)+P(z>3.214)`

`P(rejected)=0.03705+0.00065=0.0377`

If there are 500 men to enlist, the expected amount to be rejected is

`M=500*0.0377=18.85 \approx 19`