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HOME EXERCISE FOR CONTINUOUS PROBABILITY DISTRIBUTION
1. A bank manager has determined from experience that the time required for a security
guard to make his rounds in a bank building is a random variable having an
approximately normal distribution with mean = 18.0 minutes and standard deviation =
3.2 minutes. What are the probabilities that a security guard will complete his rounds
of the bank building in
a. less than 15 minutes
b. 15 to 20 minutes
c. more than 20 minutes
2. The owner of an automobile towing service company knows that the number of towing
service calls the company makes each day is a random variable having approximately
a normal distribution with the mean 36.2 and the standard deviation 5.1. What are the
probabilities that in any given day the company will make
a. exactly 30 towing service calls
b. at most 30 towing service calls
3. A television station claims that its late evening news program regularly has 35 percent
of the total viewing audience. If this claim is correct, what is the probability that
among 500 late evening viewers, more than 200 will be watching the station's news
program ?
--- END --Suggested Answers:
1a. Pr(x < 15|  = 18,  = 3.2) = Pr(z < -0.94) = 0.5 - 0.3264 = 0.1736
1b. Pr(15 x  20|  = 18,  = 3.2) = Pr(-0.94  z  0.63) = 0.3264 + 0.2357 = 0.5621
1c. Pr(x > 20|  = 18,  = 3.2) = Pr(z > 0.63) = 0.5 - 0.2357 = 0.2643
2a. Pr(29.5  x  30.5) = Pr(-1.31  z  -1.12) = 0.4049 - 0.3686 = 0.0363
2b. Pr(x  30.5) = Pr(z  -1.12) = 0.5 - 0.3686 = 0.1314
3. Pbin(x > 200| n = 500, p = 0.35) ~ Pnorm(x > 200.5|  = 175,  = 10.6654) = Pr(z >
2.39) = 0.5 - 0.4916 = 0.0084
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