The length of country and western songs is normally distribu

The length of country and western songs is normally distributed and has a mean of 200 seconds and a standard deviation of 40 seconds. Find the probability that a random selection of 40 songs will have mean length of 191.5 seconds or less. Assume the distribution of the lengths of the songs is normal.

Select one:

a. 0.86

b. 0

c. 0.09

d. 0.91

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 =    191.5      
u = mean =    200      
n = sample size =    40      
s = standard deviation =    40      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.343968006      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.343968006   ) =    0.089479367 = 0.09 [ANSWER, OPTION C]