Assume that women\'s heights are normally distributed with a mean given by mu eq
ID: 3365336 • Letter: A
Question
Assume that women's heights are normally distributed with a mean given by mu equals 63.5 in=63.5 in, and a standard deviation given by sigma equals 2.7 in=2.7 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 6464 in. (b) If 3838 women are randomly selected, find the probability that they have a mean height less than 6464 in. (a) The probability is approximately nothing. (Round to four decimal places as needed.) (b) The probability is approximately nothing. (Round to four decimal places as needed.)
Explanation / Answer
given =63.5 in, =2.7 in. The Z score to calculate probability is given by Z = (X - ) / [/Sqrt(n)]
a) P( X < 64), n =1
Z = (64-63.5)/2.7 = 0.185
The p-value ( from normal distribution tables) is 0.5735
(b) P(X<64), n = 38
Z = (64-63.5)/[2.7/sqrt(38) = 1.14
The p-value ( from normal distribution tables) is 0.8732