Question

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly​ selected, find the probability that they have a mean height between 63 and 65 inches.

Answer 1

0.9812

Explanation:

We need to find the z-score of 63 and of 65:

• z(63)=(63-63.6)/[2.5/
  `√(75)`]=-2.07846...

• z(65)=(65-63.6)/[2.5/
  `√(75)`]=4.8497...

=> P(-2.07846
`\leq`Z
`\leq`4.8497)=0.9812

So the probability that they have a mean height between 63 and 65 inches is 0.9812