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free/or 0.5$ |
| m182 | According to media research, the typical American listened to 195 hours of music in the last year. This is down from 290 hours 4 years earlier. Dick Trythall is a big country and western music fan. He listens to music while working around the house, reading, and riding in his truck. Assume the number of hours spent listening to music follows a normal probability distribution with a standard deviation of 8.5 hours.
a. If Dick is in the top 1% in terms of listening time, how many hours did he listen last year?
b. Assume that the distribution of times 4 years earlier also follows the normal probability distribution with a standard deviation of 8.5 hours. How many hours did the 1% who listen to the least music actually listen? |
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| m183 | According to the Census Bureau, 3.13 people reside in the typical American household. A sample of 25 households in Arizona retirement communities showed the mean number of residents per household was 2.86 residents. The standard deviation of this sample was 1.20 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.13 persons? |
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| m184 | According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.
a. What is the mean amount spent on insurance?
b. What is the standard deviation of the amount spent?
c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year?
d. What is the probability a family spends more than $3,000 per year? |
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| m185 | According to the Internal Revenue Service, the mean tax refund for the year 2013 was $3,000. Assume the standard deviation is $450 and that the amounts refunded follow a normal probability distribution.
a. What percent of the refunds are more than $3,100?
b. What percent of the refunds are more than $3,100 but less than $3,500?
c. What percent of the refunds are more than $2,250 but less than $3,500? |
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| m186 | According to the “January theory,” if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 29 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is .50. What is the probability this could occur by chance? You will probably need a software package such as Excel or Minitab. |
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| m187 | According to the local union president, the mean gross income of plumbers in the Salt Lake City area follows the normal probability distribution with a mean of $45,000 and a standard deviation of $3,000. A recent investigative reporter for KYAK TV found, for a sample of 120 plumbers, the mean gross income was $45,500. At the .10 significance level, is it reasonable to conclude that the mean income is not equal to $45,000? Determine the p-value. |
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| m188 | According to the South Dakota Department of Health, the number of hours of TV viewing per week is higher among adult women than adult men. A recent study showed women spent an average of 34 hours per week watching TV, and men, 29 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.5 hours and is 5.1 hours for the men.
a. What percent of the women watch TV less than 40 hours per week?
b. What percent of the men watch TV more than 25 hours per week?
c. How many hours of TV do the 1% of women who watch the most TV per week watch?
Find the comparable value for the men. |
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| m189 | Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. The mean expense is $52.0 million and the standard deviation is $11.32 million. Is it reasonable to conclude the sample data are from a population that follows a normal probability distribution? Use the .05 significance level.
Advertising Expense ($ Million) Number of Companies
25 up to 35 ............... 5
35 up to 45 ............... 10
45 up to 55 ............... 21
55 up to 65 ............... 16
65 up to 75 ............... 8
Total ................... 60 |
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| m190 | Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expenses.
Advertising Expenditure ($ millions) Number of Companies
25 up to 35............ 5
35 up to 45............ 10
45 up to 55............ 21
55 up to 65............ 16
65 up to 75............ 8
Total.............. 60 |
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| m191 | After a losing season, there is a great uproar to fire the head football coach. In a random sample of 200 college alumni, 80 favor keeping the coach. Test at the .05 level of significance whether the proportion of alumni who support the coach is less than 50%. |
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| m192 | Alexandra Damonte will be building a new resort in Myrtle Beach, South Carolina. She must decide how to design the resort based on the type of activities that the resort will offer to its customers. A recent poll of 300 potential customers showed the following results about customers’ preferences for planned resort activities:
Like planned activities ........ 63
Do not like planned activities..... 135
Not sure.............. 78
No answer............. 24
a. What is the table called?
b. Draw a bar chart to portray the survey results.
c. Draw a pie chart for the survey results.
d. If you are preparing to present the results to Ms. Damonte as part of a report, which graph would you prefer to show? Why? |
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| m193 | All eight companies in the aerospace industry were surveyed as to their return on investment last year. The results are (in percent) 10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.
(a) Range,
(b) Arithmetic mean,
(c) Variance, and
(d) Interpret the statistics. |
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| m194 | Aloha Banking Co. is studying ATM use in suburban Honolulu. A sample of 30 ATMs showed they were used the following number of times yesterday. Develop a stem-and-leaf chart. Summarize the number of times each ATM was used. What were the typical, mini-mum, and maximum number of times each ATM wasused? |
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| m195 | Althoff and Roll, an investment firm in Augusta, Georgia, advertises extensively in the Augusta Morning Gazette, the newspaper serving the region. The Gazette marketing staff estimates that 60% of Althoff and Roll’s potential market read the newspaper. It is further estimated that 85% of those who read the Gazette remember the Althoff and Roll advertisement.
a. What percent of the investment firm’s potential market sees and remembers the advertisement?
b. What percent of the investment firm’s potential market sees, but does not remember, the advertisement? |
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| m196 | An ammeter that displays three digits is used to measure current in milliamperes. |
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| m197 | Among U.S. cities with a population of more than 250,000, the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is in New York City, where the mean time is 38.3 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.5 minutes.
a. What percent of the New York City commutes are for less than 30 minutes?
b. What percent are between 30 and 35 minutes?
c. What percent are between 30 and 40 minutes? |
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| m198 | An air travel service samples domestic airline flights to explore the relationship between airfare and distance. The service would like to know if there is a correlation between airfare and flight distance. If there is a correlation, what percentage of the variation in airfare is accounted for by distance? How much does each additional mile add to the fare? The data follow.
a. Draw a scatter diagram with Distance as the independent variable and Fare as the dependent variable. Is the relationship direct or indirect?
b. Compute the correlation coefficient. At the .05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero?
c. What percentage of the variation in Fare is accounted for by Distance of a flight?
d. Determine the regression equation. How much does each additional mile add to the fare? Estimate the fare for a 1,500-mile flight.
e. A traveler is planning to fly from Atlanta to London Heathrow. The distance is 4,218 miles. She wants to use the regression equation to estimate the fare. Explain why it would not be a good idea to estimate the fare for this international flight with the regressionequation. |
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| m199 | An American Society of Investors survey found 30% of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability:
a. Exactly two of the sampled individuals have used a discount broker?
b. Exactly four of them have used a discount broker?
c. None of them has used a discount broker? |
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| m200 | An art collector is studying the relationship between the selling price of a painting and two independent variables. The two independent variables are the number of bidders at the particular auction and the age of the painting, in years. A sample of 25 paintings revealed the following sample information.
a. Develop a multiple regression equation using the independent variables number of bidders and age of painting to estimate the dependent variable auction price. Discuss the equation. Does it surprise you that there is an inverse relationship between the number of bidders and the price of the painting?
b. Create an interaction variable and include it in the regression equation. Explain the meaning of the interaction. Is this variable significant?
c. Use the stepwise method and the independent variables for the number of bidders, the age of the painting, and the interaction between the number of bidders and the age of the painting. Which variables would youselect? |
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| m201 | An auditor for Health Maintenance Services of Georgia reports 40% of policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records.
a. How many of the policyholders would you expect to have filed a claim within the last year?
b. What is the probability that 10 of the selected policyholders submitted a claim last year?
c. What is the probability that 10 or more of the selected policyholders submitted a claim last year?
d. What is the probability that more than 10 of the selected policyholders submitted a claim last year? |
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