Computer Science

CASE STUDY 4.1 – Moodle week 4

1. A bank manager wishes to provide prompt service for customers at the bank’s drive-up window. The bank currently can serve up to 10 customers per 15-minute period without significant delay. The average arrival rate is 7 customers per 15-minute period. Let x denote the number of customers arriving per 15-minute period. Assuming x has a Poisson distribution:

a Find the probability that 10 customers will arrive in a particular 15-minute period.

b Find the probability that 10 or fewer customers will arrive in a particular 15-minute period.

c Find the probability that there will be a significant delay at the drive-up window. That is, find the probability that more than 10 customers will arrive during a particular 15-minute period.

2. A telephone company’s goal is to have no more than five monthly line failures on any 100 miles of line. The company currently experiences an average of two monthly line failures per 50 miles of line. Let x denote the number of monthly line failures per 100 miles of line. Assuming x has a Poisson distribution:

a. Find the probability that the company will meet its goal on a particular 100 miles of line.

b . Find the probability that the company will not meet its goal on a particular 100 miles of line.

c . Find the probability that the company will have no more than five monthly failures on a particular 200 miles of line. A local law enforcement age

3. An extended warranty is a prolonged warranty offered to consumers by the warranty administrator, the retailer, or the manufacturer. A report in The New York Times (November 23, 2009) suggests that 20.4% of laptops fail over three years. Roberto D’Angelo is interested in an extended warranty for his laptop. A good extended warranty is being offered at Compuvest.com for $74. It will cover any repair job that his laptop may need in the next three years. Based on his research, he determines that the likelihood of a repair job in the next three years is 13% for a minor repair, 8% for a major repair, and 3% for a catastrophic repair. The extended warranty will save him $80 for a minor repair, $320 for a major repair, and $500 for a catastrophic repair. These results are summarized in the following probability distribution.

Data for Case Study – Probability Distribution for Repair Cost

Type of Repair Probability Repair Cost (in $)
None .76 0.00
Minor .13 80
Major .08 320
Catastrophic .03 500

In a report, use the above information to

1. Calculate and interpret the expected value of the repair cost.

2. Analyze the expected gain or loss for a consumer who buys the extended warranty.

3. Determine what kind of a consumer (risk neutral, risk averse, or both) will buy this extended warranty.

4. According to figures released by the New York City government, smoking among New York City teenagers is on a decline, continuing a trend that began more than a decade ago (The New York Times, January 2, 2008). According to the New York City Youth Risk Behavior Survey, the teenage smoking rate dropped to 8.5% in 2007 from about 17.6% in 2001 and 23% in 1997. City officials attribute the lower smoking rate to factors including a cigarette tax increase, a ban on workplace smoking, and television and subway ads that graphically depict tobacco-related illnesses.

In a report, use the above information to

1. Calculate the probability that at least one in a group of 10 New York City teenagers smoked in 2007.

2. Calculate the probability that at least one in a group of 10 New York City teenagers smoked in 2001.

3. Calculate the probability that at least one in a group of 10 New York City teenagers smoked in 1997.

4. Comment on the smoking trend between 1997 and 2007.

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