Assume a random sample of 100 males is selected d What is th

Assume a random sample of 100 males is selected.

(d) What is the standard deviation of the sample mean?
(e) What is the probability that the mean height of samples is less than 68 inches tall

(Problem 3) Human heights are known to be normally distributed. Men have a mean height of 70 inches and females a mean height of 64 inches. Both have a standard deviation of 3 inches. (3 points each, 15 points total) (a) Find the 1st Quartile (Q1) of the female height distribution (b) Find the height of a female in the 90th percentile (c) What is the probability that a randomly selected female is above 70 inches height?

Solution

d)

standard deviation of the mean = s / sqrt(n) = 3/sqrt(100) = 0.3 [answer]

e)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    68      
u = mean =    70      
n = sample size =    100      
s = standard deviation =    3      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -6.666666667      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -6.666666667   ) =    0.0000000000130839