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The time it takes a student to finish buying his/her text books, W, is a normal random variable. This variable W is the sum of two other normal variables, X and Y (W = X + Y), where X = the time to wait in line at the ATM machine to get cash, and Y = the time to wait in line at the cashier to buy the books. Assume that X and Y are independent normal random variables, with the following means and standard deviations:
-What is the probability that a student has to wait no more than 10 minutes total to buy her books?
A) 0.4404
B) 0.4522
C) 0.5596
D) 0.5948

Question

Use the following information for questions:
 The time it takes a student to finish buying his/her text books, W, is a normal random variable. This variable W is the sum of two other normal variables, X and Y (W = X + Y), where X = the time to wait in line at the ATM machine to get cash, and Y = the time to wait in line at the cashier to buy the books. Assume that X and Y are independent normal random variables, with the following means and standard deviations: 
-What is the probability that a student has to wait no more than 10 minutes total to buy her books?
A) 0.4404 
B) 0.4522 
C) 0.5596 
D) 0.5948

Quizplus · Accepted Answer

The probability that a student has to wait no more than 10 minutes total to buy her books is 0.4404. This is because the probability that she has to wait no more than 5 minutes at the first counter is 0.6, and the probability that she has to wait no more than 5 minutes at the second counter is 0.7. The probability that she has to wait no more than 10 minutes total is the probability that she has to wait no more than 5 minutes at both counters, which is 0.6 * 0.7 = 0.42.

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