Question

Suppose that the weight of male babies less than 2 months old is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. A sample of 36 babies is selected. What is the probability that the average weight of the sample is less than 11.13 pounds?

Answer 1

For sampling distribution of mean, P( < A) = P(Z < (A - mean)/standard error)

Mean, = 11.5 pounds

Standard deviation, = 2.7 pounds

Sample size, n = 36

Standard error =

=

= 0.45

P(the average weight of the sample is less than 11.13 pounds) = P( < 11.13)

= P(Z < (11.13 - 11.5)/0.45)

= P(Z < -0.82)

= 0.2061