The average retail price of gasoline all types for the first

The average retail price of gasoline (all types) for the first half of 2009 was 236.5 cents with a standard deviation of 31.5 cents. A random sample of gas prices was taken from 49 locations. What is the probability that the mean of the sample was less than 230 cents?

Select one:

a. 0.418

b. 0.074

c. 0.926

d. 0.582

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 =    230      
u = mean =    236.5      
n = sample size =    49      
s = standard deviation =    31.5      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.444444444      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.444444444   ) =    0.074306998 = 0.074 [ANSWER, OPTION B]