A sample of 9 bulldogs is taken from a large population of f

A sample of 9 bulldogs is taken from a large population of frogs with normally distributed croaking volumes. If the sample of frogs has a mean croaking volume of x = 66.0455 dB with variance s^2 = 30.60, what is the probability that the population has an average croaking volume of mu = 59 dB or more?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    59      
u = mean =    66.0455      
          
s = standard deviation =    6.3      
          
Thus,          
          
z = (x - u) / s =    -1.118333333      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.118333333   ) =    0.868287672 [ANSWER]