Question

In a certain city, heights of young men are distributed normally with a mean of 173 centimeters and a standard deviation of 30 centimeters.

A. Find the probability that a randomly selected man from this city is taller than 190 centimeters.

B. Find the probability that the mean height of 16 randomly selected men from this city is taller than 190 centimeters.

Answer 1

Solution :

(a)

P(x > 190) = 1 - P(x < 190)

= 1 - P[(x - ) / < (190 - 173) / 30]  

= 1 - P(z < 0.567)

= 0.2854

(b)

= / n = 30 / 16 = 7.5

P( > 190) = 1 - P( < 190)

= 1 - P[( - ) / < (190 - 173) / 7.5]

= 1 - P(z < 2.267)

= 0.0117