Question

In a large group of men 4% are under 160cm tall and 52% are between 160cm and 175cm tall. Assuming that the heights of men are normally distributed, what are the mean and standard deviation of the distribution?

Answer 1

Let shows the mean and shows the population standard deviation.

We need z-score that has 0.04 area to its left. The z-score -1.75 has 0.04 area to its left.

Let X is a random variable shows the height. So,

.............(i)

Since 4% are under 160cm tall and 52% are between 160cm and 175cm tall so 52%+4% = 56% are under 175 cm.

We need z-score that has 0.56 area to its left. The z-score 0.151 has 0.56 area to its left.

So,

.......(ii)

Subtracting equation (i) from (ii) gives

Putting this in equation (i) gives

Answers: Mean = 173.72, SD = 7.8947