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 60 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 160 and 180 cm tall?


(b) How many would you expect to be taller than 165 cm?

Answer 1

Given,

= 170 , = 5

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

a)

P(160 < X < 180) = P(X < 180) - P(X < 160)

= P(Z < (180 - 170) / 5) - P(Z < (160 - 170) / 5)

= P(Z < 2) - P(Z < -2)

= 0.9772 - 0.0228

= 0.9544

Of the 60 people we expect = 0.9544 * 60 = 57 people

b)

P(X > 165) = P(Z > (165 - 170) / 5)

= P(Z > -1)

= P(Z < 1)

= 0.8413

Of the 60 people we expect = 0.8413 * 60 = 50 people