Question

1. It is known that the birth weight of newborn babies in the U.S. has a mean of 7.1 pounds with a standard deviation of 1.5 pounds. Suppose we randomly sample 36 birth certificates from the State Health Department, and record the birth weights of these babies.

  

1. The sampling distribution of the average birth weights of random samples of 36 babies has a mean equal to ______ pounds and a standard deviation of ______ pounds.

2. What is the probability the average birth weight of a random sample of 36 babies is less than 7.7 pounds? _______

What is the probability the average birth weight of a random sample of 36 babies is between 6.9 pounds and 7.5 pounds? _______

Answer 1

Mean of sampling distribution of Sample mean  = = 7.1

Standard deviation of sampling distribution = / sqrt(n) = 1.5 / sqrt(36) = 0.25

Using central limit theorem ,

P( < x) = (Z < (x - ) / ( / sqrt(n) ) )

So,

P( < 7.7) = P(Z < (7.7 - 7.1) / 0.25 )

= P(Z < 2.4)

= 0.9875

P(6.9 < < 7.5) = P( < 7.5) - P( < 6.9)

= P(Z < (7.5 - 7.1) / 0.25) - P(Z < (6.5 - 7.1) / 0.25)

= P(Z < 1.6) - P(Z < -2.4)

= 0.9452 - 0.0082

= 0.9370