Statistics functions

Question

Assume that women's heights are normally distributed with a mean given by mu equals 62.4 inμ=62.4 in,
and a standard deviation given by sigma equals 2.6 inσ=2.6 in.
(a) If 1 woman is randomly selected, find the probability that her height is less than 6363
in.
(b) If 3838
women are randomly selected, find the probability that they have a mean height less than 6363
in.
(a)
The probability is approximately  

Answer 1

I guess you meant 63.63 inches. 63.63- 62.4 = 1.23; Compute 1.23/2.6 = .47 standard deviations. So, look at your normal table for the value corresponding to that amount of std deviations.

 

If 3,838 women are selected at random the probability that there mean height would be less that 63.63 is 100%. that is because you take the standard deviation and divide it by the sqr of 3838.