Question

the mean weight of adult males is 165 pounds with a standard deviation of 30 pounds. if a sample of 35 adult males is selected, find the probability that the mean of the sample will be less than 155 pounds

Answer 1

0.5244 is the answer.

Explanation:

Given that the mean weight of males adult is 165 pounds.

Std deviation is 30 pounds

Sample size n = 35

Hence sample std deviation = 30/sq rt 35 = 5.071

Then X bar the mean of the sample follows a normal distribution

X bar : N(165, 5.071) by central limit theorem

Required probability =P(X<155)

When x =155, Z =
`(155-165)/(5.071) =-1.972`

Hence P(X<155) = P(Z<-1.972) = 0.5-0.4756

= 0.5244