SECTION - D

183) Suppose you know that the number of complaints coming into a phone center averages 3 every ten minutes. Assume that the number of calls follows the Poisson distribution. What is the probability that there are exactly three calls during the next ten minutes?

184) An auditor reviewing the invoices of a small company finds that there are errors in 1.5% of them. If the auditor looks at 500 invoices, what is the probability that he finds more than 3 invoices with errors? Use the Poisson approximation to the binomial distribution.

185) The number of accidents on a US -131 highway average 4.4 per year. Assuming that the number of accidents follows a Poisson distribution, what is the probability that there are more than three accidents next year on US - 131?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

As a purchasing agent, you are responsible for selecting sources of supply for manufactured components to use in your firm's production process. The salesman for a certain supplier has indicated that they can supply an electronic sub-assembly that has a defect rate of 1.1%-well below your current supplier's defect rate. You accept 100 sub-assemblies for evaluation, and find that there were four defects.

186) Using the Poisson approximation to the binomial, how likely is it to get four or less defects out of 100?

187) Using the Poisson approximation to the binomial, how likely is it to get exactly four defects out of 100?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

It has been reported that 1.7% of the work force will retire this year. Consider a random sample of 200 workers.

188) What is the probability that more than three of them will retire this year? Use the Poisson approximation to the binomial.

189) What is an estimate of the standard deviation of the number of people who will retire this year? Use the Poisson approximation to the binomial.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

From past experience, it is known 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year-olds is given this voice recognition test.

190) Find the probability at least 3 children do not recognize their mother's voice.

191) Find the probability all 20 children recognize their mother's voice.

192) Let the random variable X denote the number of children who do not recognize their mother's voice. Find the mean of X.

193) Let the random variable X denote the number of children who do not recognize their mother's voice. Find the variance of X.

194) Find the probability that at most 4 children do not recognize their mother's voice?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. A random sample of 25 customers is selected. Assume that customers' purchases are made independently, and let X represent the number of customers who purchase running shoes. (Hint: Solve using Excel.)

195) What is the probability that exactly 18 customers purchase running shoes?

196) What is the probability that no more than 19 customers purchase running shoes?

197) What is the probability that at least 17 customers purchase running shoes?

198) What is the probability that between 17 and 21 customers, inclusively, purchase running shoes?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:

The number of people arriving at a bicycle repair shop follows a Poisson distribution with an average of 5 arrivals per hour. Let X represent the number of people arriving per hour.

199) What is the probability that seven people arrive at the bike repair shop in a one hour period of time?

200) What is the probability that at most seven people arrive at the bike repair shop in a one hour period of time?

201) What is the probability that more than seven people arrive at the bike repair shop in a one hour period of time?

202) What is the probability that between 4 and 9 people, inclusively, arrive at the bike repair shop in a one hour period of time?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:

You have recently joined a country club. The number of times you expect to play golf in a month is represented by a random variable with a mean of 10 and a standard deviation of 2.2. Assume you pay monthly membership fees of $500 per month and pay an additional $50 per round of golf.

203) What is your average monthly bill from the country club?

A) $700

B) $800

C) $900

D) $1000

204) What is the standard deviation for your average monthly bill from the country club?

A) $220

B) $110

C) $324

D) $180

205) Which of the following is false regarding the normal distribution?

A) The mean, median, and mode are equal.

B) The frequency of values peaks at the mean, regardless of the value of the mean or variance.

C) 100% of the values fall between 3 standard deviations.

D) The shape of the distribution is symmetrical around the mean.

206) One normal distribution has a mean of 5 and a standard deviation of 2. A second normal distribution has a mean of 6 and a standard deviation of 1. Which of the following statements is true?

A) The width of the first distribution is wider than the second distribution.

B) The central location of the first distribution is higher than the second distribution.

C) The dispersions of both distributions are the same.

D) The locations of both distributions are the same.

207) Let the random variable Z follow a standard normal distribution. Find the value k, such

that P(Z > k) = 0.73.

A) 0.27

B) 0.73

C) -0.16

D) -0.61