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Find the expected number based on z score

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 165 and a standard deviation of 6. We find the heights of 40 people.

(a) How many would you expect to be between 157 and 173 cm tall?

(b) How many would you expect to be taller than 160 cm?

For a particular value, this table gives the percent of scores between the mean and the z-value of a normally distributed random variable. What percent of the total population is found between the mean and the z-score, assume z = 2.93.

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HI there,

Here is my answer:

(a) ...

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The solution provides detailed explanation how to find out the expected number based on z score.

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