Question

The mean weight of a 2-year old is 27.5 pounds with a standard deviation of 2.3 pounds, although some 2-year olds weigh as much as 39 pounds. A health official randomly selects the medical records of 50 2-year olds to study. What is the probability the mean weight of the health official’s sample is more than 28.5 pounds?   

A) 0.001 B) 0.332 C) 0.668 D) 0.999 E) This cannot be determined because the distribution is skewed right due to the 2-year olds that weigh as much as 39 pounds.

Answer 1

= 27.5 pounds

= 2.3 pounds'

n = 50

Since the sample is sufficiently large (>30), we can expect the sampling distribution of mean to be approximately normal.

P( < A) = P(Z < (A - )/)

= = 27.5 pounds

=

= 2.3/50

= 0.3253

P(mean weight of the health official’s sample is more than 28.5 pounds) = P( > 28.5)

= 1 - P( < 28.5)

= 1 - P(Z < (28.5 - 27.5)/0.3253)

= 1 - P(Z < 3.07)

= 1 - 0.9989

= 0.001 (option A)