Question

Birth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation of 15 oz. You take a random sample of babies born at the hospital and find the mean weight. What is the probability that the mean weight will be between 111 and 114 in a sample of 50 babies born at this hospital? Round to 3 decimal places.

Answer 1

X : birth weights are normally distributed with = 110 Oz and standard deviation = 15 Oz

If n = 50 we asked P( 111 < xbar < 114)

P( 111< xbar < 114) =P[111 - )//√n < (xbar - )//√n < (114 - )/(/√n)]

P( 111 < xbar < 114) = P( 0.47 < Z < 1.89)

= P( Z < 1.89) - P( Z < 0.47)

= 0.9706 - 0.6808

P(111 < xbar < 114) = 0.290