The length of country and western songs has a mean of 200 se

The length of country and western songs has a mean of 200 seconds and a standard deviation of 40 seconds. Find the probability that a random selection of 20 songs will have mean length of 186.30 seconds or less.

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 =    186.3      
u = mean =    200      
n = sample size =    20      
s = standard deviation =    40      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.531706565      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.531706565   ) =    0.062797431 [ANSWER]

This option is not one of the choices, but is indeed the correct answer. Please report this problem to your instructor.