Question

In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 4 inches. Out of the 1401 boys who go to that school, how many would be expected to be between 68 and 74 inches tall, to the nearest whole number?

Answer 1

To solve this problem, we first need to standardize the values of interest using the standard normal distribution formula:

z = (x - mu) / sigma

where x is the value of interest, mu is the mean, sigma is the standard deviation, and z is the standardized value.

For x = 68, z = (68 - 69) / 4 = -0.25

For x = 74, z = (74 - 69) / 4 = 1.25

Using a standard normal distribution table, we can find the proportion of the population that falls between these two values:

P(-0.25 < z < 1.25) = P(z < 1.25) - P(z < -0.25) = 0.8944 - 0.4013 = 0.4931

Finally, we can multiply this proportion by the total number of boys to find the expected number of boys between 68 and 74 inches tall:

Expected number = 0.4931 * 1401 = 690.