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

= 110, = 15

n= 50

We want to find P( 111 <   < 114 )

Where P( 111 <   < 114 ) = P( < 114 ) - P( < 111 )

first find P( < 114 )

formula for z-score is

z = 1.8856

z = 1.89

P( < 114 ) = P(z < 1.89)

using normal z table we get the

P(z < 1.89) =  0.9703

P( < 114 ) = 0.9703

now find P( < 111 )

formula for z-score is

z = 0.4714

z = 0.47

P( < 111 ) = P(z < 0.47)

using normal z table we get the

P(z < 0.47) =  0.6813

P( < 111 ) = 0.6813

P( 111 <   < 114 ) = P( < 114 ) - P( < 111 )

P( 111 <   < 114 ) =  0.9703 − 0.6813

P( 111 <   < 114 ) = 0.289

probability that the mean weight will be between 111 and 114 in a sample of 50 babies born at this hospital is = 0.289

Answer = 0.289