The contents of bottles of water have a distribution with me

The contents of bottles of water have a distribution with mean 9.1 ounces and standard deviation .3 ounce. Suppose a sample of size 64 will be taken and the sample mean will be calculated. What is the probability that the mean of the sample is more than 9 ounces?

Select one:

a. .0038

b. .3694

c. .6306

d. .9962

e. Cannot be determined

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    9      
u = mean =    9.1      
n = sample size =    64      
s = standard deviation =    0.3      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.666666667      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -2.666666667   ) =    0.996169619 = 0.9962 [OPTION D, ANSWER]