Question

Adult male height is normally distributed with a mean of 69.2 inches and a standard deviation of 2.28 inches.

a) If an adult male is randomly selected, what is the probability that the adult male has a height greater than 69.1 inches? Round your final answer to four decimal places.

b) If 28 adult male are randomly selected, what is the probability that they have a mean height greater than 70 inches? Round your final answer to four decimal places.

Answer 1

Solution :

Given ,

mean = = 69.2

standard deviation = = 2.28

P(x >69.1 ) = 1 - P(x<69.1 )

= 1 - P[ X - / / (69.1-69.2) /2.28 ]

= 1 - P(z <-0.04 )

Using z table

= 1 - 0.4840

= 0.5160

probability= 0.5160

(B)

n = 28

= 69.2

= / n =2.28 / 28 = 0.4309

P( > 70) = 1 - P( <70 )

= 1 - P[( - ) / < (70-69.2) / 0.4309 ]

= 1 - P(z <1.86 )

Using z table

= 1 - 0.9686

= 0.0314

probability= 0.0314