Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The average price for a gallon of gasoline in the United States is $3.73 and in

ID: 3135176 • Letter: T

Question

The average price for a gallon of gasoline in the United States is $3.73 and in Russia it is $3.40 (Bloomberg Businessweek, March 5–March 11, 2012). Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $.25 in the United States and a standard deviation of $.20 in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon? b. What percentage of the gas stations in Russia charge less than $3.50 per gallon? c. What is the probability that a randomly selected gas station in Russia charged more than the mean price in the United States?

Explanation / Answer

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    3.5      
u = mean =    3.73      
          
s = standard deviation =    0.25      
          
Thus,          
          
z = (x - u) / s =    -0.92      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.92   ) =    0.17878638 [ANSWER]

**************************

B)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    3.5      
u = mean =    3.4      
          
s = standard deviation =    0.2      
          
Thus,          
          
z = (x - u) / s =    0.5      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   0.5   ) =    0.691462461 = 69.15% [ANSWER]

**************************

c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    3.73      
u = mean =    3.4      
          
s = standard deviation =    0.2      
          
Thus,          
          
z = (x - u) / s =    1.65      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.65   ) =    0.049471468 [ANSWER]

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote