Question

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. (You may need to use the standard normal distribution table. Round your answers to the nearest whole number.)

(a) How many would you expect to be between 170 and 175 cm tall?


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

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 170

Standard deviation = 5

a) P(between 170 and 175) = P(X < 175) - P(X < 170)

= P(Z < (175 - 170)/5) - P(Z < (170 - 170)/5)

= P(Z < 1) - P(Z < 0)

= 0.8413 - 0.5

= 0.3413

Number of people expected to be between 170 and 175 cm tall = 80x0.3413 = 27

b) P(taller than 177) = 1 - P(X < 177)

= 1 - P(Z < (177 - 170)/5)

= 1 - P(Z < 1.4)

= 1 - 0.9192

= 0.0808

Number of people expected to be taller than 177 = 80x0.0808 = 6