Question

The heights of South African men are normally distributed with a mean of 69 inches and a standard deviation of 4 inches. What is the probability that a randomly selected South African man is taller than 72 inches (sample size of 1)?   What is the probability that a sample of 100 has a mean greater than 72 inches?

Answer 1

Solution :

Given that ,

mean = = 69

standard deviation = = 4

a) P(x > 72) = 1 - p( x< 72)

=1- p P[(x - ) / < (72 - 69) / 4]

=1- P(z < 0.75 )

Using z table,

= 1 - 0.7734

= 0.2266

b) n = 100

= = 69

= / n = 4 / 100 = 0.4

P( > 72) = 1 - P( < 72)

= 1 - P[( - ) / < (72 - 69) / 0.4 ]

= 1 - P(z < 7.5)

Using z table,    

= 1 - 1

= 0