The mean height of women in a country ages 20 29 is 63 5 in

The mean height of women in a country (ages 20 - 29) is 63 5 inches A random sample of 66 women m this age group is selected What is the probability that the mean height tor the sample is greater than 64 inches? Assume sigma = 2/4 The probability that the mean height for the sample is greater than 64 inches is

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    64      
u = mean =    63.5      
n = sample size =    65      
s = standard deviation =    2.74      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.471214918      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.471214918   ) =    0.070616502 [ANSWER]