the mean height of this sample is between 29.5 inches and 31.5 inches

Question

The heights of 12 month -old boys are approximately normally distributed with a mean of 29.8 inches and a standard deviation of 1.2 inches A sample of thirty six 12 month- old boys was taken. Find the probability of each of the of the following:

Answer 1

For a height H inches, Z=(H-29.8)/1.2.

Let Z₁=(29.5-29.8)/1.2=-0.3/1.2=-0.25; Z₂=(31.5-29.8)/1.2=1.7/1.2.

P(Z₂)-P(Z₁)=0.9217-0.4013=0.5204 or 52.04% probability of height between 29.5 and 31.5 inches.