Mean and deviation

Question

assume that women’s heights are normally distributed with a mean by 64.5 in, and a standard deviation given by 2.6in. 

  (A) If 1 woman is randomly selected, find the probability that her height is less than 65 in. 

  (B) If 35 women are randomly selected, find the probability that they have a mean height less than 65 in. 

Answer 1

Hi Kate,

 

A) find the z value

 

(65 - 64.5)/2.6 = .19

 

p(z<.19) = .5753

 

or 57.53%

 

B) to find the z value using the mean of a sample

 

z = (mean of sample - mean of population)/(stand dev/√n)

 

z = (65 - 64.5)/ (2.6/√35) = 1.14

 

p(z<1.14) = .8729

 

or 87.29%

 

hope this helps