# Solving set of questions on descriptive statistics

Question 1

1. A major U.S. automaker has determined that the city mileage for one of its new SUV models is normally distributed with a mean equal to 15.2 mpg. A report issued by the company indicated that 22 percent of the SUV model vehicles will get more than 17 mpg in the city. Given this information, what is the city mileage standard deviation for this SUV model?

Answer

0.77 mpg

Approximately 2.34 mpg

1.8 mpg

Approximately 3.1 mpg

1 points

Question 2

1. A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. As a promotion, the company plans to hold a drawing to give away one free vacation to Hawaii for a customer who uses between 400 and 402 minutes during a particular month. Based on the information provided, what proportion of the company's customers would be eligible for the drawing?

Answer

Approximately 0.1026

About 0.004

Approximately 0.2013

About 0.02

1 points

Question 3

1. A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. The company is thinking of changing its fee structure so that anyone who uses the phone less than 250 minutes during a given month will pay a reduced monthly fee. Based on the available information, what percentage of current customers would be eligible for the reduced fee?

Answer

About 36.4 percent

Approximately 52 percent

About 86.6 percent

About 13.6 percent

1 points

Question 4

1. A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes. The company is thinking of charging a lower rate for customers who use the phone less than a specified amount. If it wishes to give the rate reduction to no more than 12 percent of its customers, what should the cut-off be?

Answer

About 237 minutes

About 654 minutes

About 390 minutes

About 325 minutes

1 points

Question 5

1. A professor noted that the grades of his students were normally distributed with a mean of 75.07 and a standard deviation of 11.65. If only 10 percent of the students received grades of A, what is the minimum score needed to receive an A?

Answer

80.00

85.00

90.00

95.00

1 points

Question 6

1. A recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours. Given this information, what is the probability that a deliberation will last between 10 and 15 hours?

Answer

Approximately 0.29

Nearly 0.75

About 0.48

About 0.68

1 points

Question 7

1. Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. Based on this information, what is the probability that an employee will have less than 20 minutes of unused sick time?

Answer

0.002

0.966

0.063

0.042

1 points

Question 8

1. Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. Based on this information, what is the probability that three randomly chosen employees have over 400 unused sick minutes at the end of the year?

Answer

0.1667

0.0046

0.5001

0.0300

1 points

Question 9

1. Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over 400 minutes of sick leave at the end of the year. What percentage of employees could expect a cash payment?

Answer

16.67 percent

0.1667 percent

Just over 43 percent

80 percent

1 points

Question 10

1. Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over a specified amount of sick leave minutes. Assuming that the company wishes no more than 5 percent of all employees to get a cash payment, what should the required number of minutes be?

Answer

24 minutes

419 minutes

456 minutes

470 minutes

1 points

Question 11

1. It is assumed that the time customers spend in a record store is uniformly distributed between 3 and 12 minutes. Based on this information, what is the probability that a customer will be exactly 7.50 minutes in the record store?

Answer

0.1250

0.05

Essentially zero

0.111

1 points

Question 12

1. It is assumed that the time customers spend in a record store is uniformly distributed between 3 and 12 minutes. Based on this information, what is the probability that a customer will spend more than 9 minutes in the record store?

Answer

0.33

0.1111

0.67

0.25

1 points

Question 13

1. It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. Based on this information, what is the probability that a randomly selected part will fail in less than 10 hours?

Answer

About 0.82

About 0.20

About 0.33

About 0.18

1 points

Question 14

1. It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. If one extra component is installed as a backup, what is the probability of at least one of the two components working for at least 60 hours?

Answer

About 0.51

About 0.09

About 0.06

About 0.70

1 points

Question 15

1. It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. What is the probability that a component will be functioning after 60 hours?

Answer

Approximately 0.30

About 0.70

About 0.21

About 0.49

1 points

Question 16

1. It is thought that the time between customer arrivals at a fast food business is exponentially distributed with equal to 5 customers per hour. Given this information, what is the mean time between arrivals?

Answer

12 minutes

5 minutes

5 hours

2 minutes

1 points

Question 17

1. Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. Based on this information, what is the probability of a student reading at more than 1400 words per minute after finishing the course?

Answer

0.0202

0.5207

0.4798

0.9798

1 points

Question 18

1. Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. If two students were selected at random, what is the probability that they would both read at less than 400 words per minute?

Answer

0.4938

0.0062

0.00004

0.2438

1 points

Question 19

1. Suppose that it is believed that investor returns on equity investments at a particular brokerage house are normally distributed with a mean of 9 percent and a standard deviation equal to 3.2 percent. What percent of investors at this brokerage hour earned at least 5 percent?

Answer

89.44 percent

10.56 percent

39.44 percent

100 percent

1 points

Question 20

1. The makers of Sweet-Things candy sell their candy by the box. Based on company policy, the mean target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy. In order to do this, what should the mean fill weight be set to if the fill standard deviation is 0.13 pounds? Assume that the box weights are normally distributed.

Answer

Just over 2 pounds

Approximately 2.33 pounds

Nearly 1.27 pounds

Approximately 1.86 pounds

1 points

Question 21

1. The makers of Sweet-Things candy sell their candy by the box. Based on company policy, the mean target weight of all boxes is 2.0 pounds. To make sure that they are not putting too much in the boxes, the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy. In order to do this, with a mean weight of 2 pounds, what must the standard deviation be? Assume that the box weights are normally distributed.

Answer

Approximately 0.05 pounds

-0.133 pounds

1.144 pounds

None of these.

1 points

Question 22

1. The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a standard deviation equal to $80. Based on this information, what are the chances that the revenue on the first show will be between $300 and $500?

Answer

About 0.3062

Approximately 0.6534

0.1736

Approximately 0.4798

1 points

Question 23

1. The manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456. Based on this information, what are the chances that the revenue on the first show will exceed $800?

Answer

0.1255

Essentially zero

0.3745

0.9999

1 points

Question 24

1. The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. The manager has decided to have a signal system attached to the phone so that after a certain period of time, a sound will occur on her employees' phone if she exceeds the time limit. The manager wants to set the time limit at a level such that it will sound on only 8 percent of all calls. The time limit should be:

Answer

10.35 minutes.

approximately 5.19 minutes.

about 14.58 minutes.

about 11.23 minutes.

1 points

Question 25

1. The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. What is the probability that three randomly monitored calls will each be completed in 4 minutes or less?

Answer

0.4756

Approximately 0.1076

About 0.00001

Can't be determined without more information.

1 points

Question 26

1. The time between calls to an emergency 911-call center is exponentially distributed with a mean time between calls of 645 seconds. Based on this information, what is the probability that the time between the next two calls is between 200 and 400 seconds?

Answer

Approximately 0.47

About 0.199

About 0.747

About 0.801

1 points

Question 27

1. The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state's turnpike is exponentially distributed with = 4 cars per minute. Based on this information, the probability that it will take exactly 30 seconds between arrivals is:

Answer

0.0006

0

0.9994

0.25

1 points

Question 28

1. The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state's turnpike is exponentially distributed with = 4 cars per minute. Based on this information, what is the probability that the time between any two cars arriving will be less than half a minute?

Answer

Approximately 1.0

Approximately 0

about 0.86

About 0.75

1 points

Question 29

1. Which of the following is not a characteristic of the normal distribution?

Answer

Symmetric

Mean=median=mode

Bell-shaped

Equal probabilities at all values of x

1 points

Question 30

1. Which of the following probability distributions would most likely be used to describe the time between failures for electronic components?

Answer

Binomial distribution

Exponential distribution

Uniform distribution

Normal distribution

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#### Solution Summary

The solution gives detailed steps on computing different terms on descriptive statistics including standard deviation, proportion, percentile, probability and sample size.

The solution gived detailed steps on solving some questions on the topic of descriptive statistics. All formula and calculations are shown and explained.

I need help with both of these problems. I have tried everything and I can't figure it out.

Problem Set # 6.54. A new dental bonding agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called Smartbond) has been developed to eliminate the necessity of a dry field. However there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive (Trends in Biomaterials & Artificial Organs, Jan. 2003). Tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x bar = 5.07 Mpa and a standard deviation of s= .46 Mpa. Orthodontists want to know if the mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, the mean breaking strength of the composite adhesive.

a. Set up the null and alternative hypotheses for the test.

b. Find the rejection region for the test using significance level=.01.

c. Compute the test statistic.

d. Give the appropriate conclusion for the test.

e. What conditions are required for the test results to be valid?

Problem Set #7.30. Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, Summer 2008), where evaluation scores ranged from 12 (lowest) to 60 (highest). The PARS file contains the 2007 and 2008 evaluation scores for all 24 agencies. (See Exercise 2.123, p.94). Data for a random sample of five of these agencies are shown in the accompanying table. Suppose you want to conduct a paired-difference test to determine whether the true mean evaluation score of government agencies in 2008 exceeds the true mean evaluation score in 2007.

Agency Score07 Score08

GSA 34 40

Agriculture 33 35

Social Security 33 33

USAID 32 42

Defense 17 32

a. Explain why the data should be analyzed using a paired-difference test.

b. Compute the difference between the 2008 score and the 2007 score for each sampled agency.

c. Find the mean and standard deviation of the differences, part b.

d. Use the summary statistics, part c, to find the test statistic.

e. Give the rejection region for the test using significance level=.10.

f. Make the appropriate conclusion in words of the problem.