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Chapter 5: 5-47E (page 321)

Question: Hotel guest satisfaction. Refer to the results of the 2015 North American Hotel Guest Satisfaction Index Study, Exercise 4.49 (p. 239). Recall that 15% of hotel guests were 鈥渄elighted鈥� with their experience (giving a rating of 10 out of 10); of these guests, 80% stated they would 鈥渄efinitely鈥� recommend the hotel. In a random sample of 100 hotel guests, find the probability that fewer than 10 were delighted with their stay and would recommend the hotel.

Short Answer

Expert verified

The probability that fewer than 10 () delighted with their stay and would recommend the hotel is 0.2676.

Step by step solution

01

Given information

Let p denotes the proportion of guests who were delighted with their stay and would recommend the hotel.

15% of guests were delighted with their experience, and of these, 80% would recommend the hotel

Therefore,

.

A random sample of size 100 is selected.

02

Computing the required probability

The probability that fewer than 10 () delighted with their stay and would recommend the hotel obtain as follows

Pp^<.10=Pp^-p蟽p^<0.10-p蟽p^=PZ<0.10-0.120.12脳0.88100=PZ<-0.020.001056=PZ<-0.020.0324=PZ<-0.62=0.2676

In the z-table, the value at the intersection of -0.60 and 0.02 is the required probability.

Therefore, the required probability is 0.2676.

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Most popular questions from this chapter

Use the computer to generate 500 samples, each containing n = 25 measurements, from a population that contains values of x equal to 1, 2, . . 48, 49, 50 Assume that these values of x are equally likely. Calculate the sample mean (蠂炉) and median m for each sample. Construct relative frequency histograms for the 500 values of (蠂炉)and the 500 values of m. Use these approximations to the sampling distributions of (蠂炉)and m to answer the following questions:

a. Does it appear that and m are unbiased estimators of the population mean? [Note:渭=25.5]

b. Which sampling distribution displays greater variation?

Consider the population described by the probability distribution shown below.

The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as shown below.

a. Find the sampling distribution of the sample meanx.

b. Construct a probability histogram for the sampling distribution ofx.

c. What is the probability thatxis 4.5 or larger?

d. Would you expect to observe a value ofxequal to 4.5 or larger? Explain.

Switching banks after a merger. Banks that merge with others to form 鈥渕ega-banks鈥� sometimes leave customers dissatisfied with the impersonal service. A poll by the Gallup Organization found 20% of retail customers switched banks after their banks merged with another. One year after the acquisition of First Fidelity by First Union, a random sample of 250 retail customers who had banked with First Fidelity were questioned. Letp^ be the proportion of those customers who switched their business from First Union to a different bank.

  1. Find the mean and the standard deviation of role="math" localid="1658320788143" p^.
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  3. If samples of size 250 were drawn repeatedly a large number of times and determined for each sample, what proportion of the values would fall within the interval you calculated in part c?

Rental car fleet evaluation. National Car Rental Systems, Inc., commissioned the U.S. Automobile Club (USAC) to conduct a survey of the general condition of the cars rented to the public by Hertz, Avis, National, and Budget Rent-a-Car.* USAC officials evaluate each company鈥檚 cars using a demerit point system. Each car starts with a perfect score of 0 points and incurs demerit points for each discrepancy noted by the inspectors. One measure of the overall condition of a company鈥檚 cars is the mean of all scores received by the company (i.e., the company鈥檚 fleet mean score). To estimate the fleet mean score of each rental car company, 10 major airports were randomly selected, and 10 cars from each company were randomly rented for inspection from each airport by USAC officials (i.e., a sample of size n = 100 cars from each company鈥檚 fleet was drawn and inspected).

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d. Refer to part c. The company claims that their true fleet mean score 鈥渃ouldn鈥檛 possibly be as high as 30.鈥� The sample mean score tabulated by USAC for this company was 45. Does this result tend to support or refute the claim? Explain.

Suppose a random sample of n measurements is selected from a population with u=100mean and variance role="math" localid="1657967387987" 蟽2=100. For each of the following values of n, give the mean and standard deviation of the sampling distribution of the sample mean.

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