Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 80 people.

(a) How many would you expect to be between 170 and 180 cm tall?

a) between 170 and 180 is 2 standard deviations

according to the normal distribution curve, 2 standard deviations represents

47.7% of the total distribution, so

(80)(.477) = 38

The second part to the problem is below.

(b) How many would you expect to be taller than 177 cm?

z = 177-170 / 5 = 1.4

P(z>1.4) = 1 - .9192 = .08

(80)(.08) = 6

Thank you for the answer to both parts, great work.

You're welcome.

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