Chapter 6&7

The proportion of items in a population that possess a specific attribute is known to be 0.70. If a simple random sample of size n = 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.65, what is the sampling error? -0.03 0.08 -0.05 0.01

-0.05

The branch manager for United Savings and Loan in Seaside, Virginia, has worked with her employees in an effort to reduce the waiting time for customers at the bank. Recently, she and the team concluded that average waiting time is now down to 3.5 minutes with a standard deviation equal to 1.0 minute. However, before making a statement at a managers' meeting, this branch manager wanted to double-check that the process was working as thought. To make this check, she randomly sampled 25 customers and recorded the time they had to wait. She discovered that mean wait time for this sample of customers was 4.2 minutes. Based on the team's claims about waiting time, what is the probability that a sample mean for n = 25 people would be as large or larger than 4.2 minutes? 0.0231 0.0214 0.0000 0.0512

0.0000

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? 85.00 90.00 95.00 80.00

90.00

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? Approximately 0.1076 0.4756 About 0.00001 Can't be determined without more information.

About 0.00001

A major shipping company has stated that 96 percent of all parcels are delivered on time. To check this, a random sample of n = 200 parcels were sampled. Of these, 184 arrived on time. If the company's claim is correct, what is the probability of 184 or fewer parcels arriving on time? Just over 0.98 About 0.0019 About 0.4981 Nearly 0.24

About 0.0019

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? Essentially zero 0.1255 0.3745 0.9999

Essentially zero

The J R Simplot Company is one of the world's largest privately held agricultural companies, employing over 10,000 people in the United States, Canada, China, Mexico, and Australia. More information can be found at the company's Web site: www.Simplot.com. One of its major products is french fries that are sold primarily on the commercial market to customers such as McDonald's and Burger King. French fries have numerous quality attributes that are important to customers. One of these is called "dark ends," which are the dark-colored ends that can occur when the fries are cooked. Suppose a major customer will accept no more than 0.06 of the fries having dark ends. Recently, the customer called the Simplot Company saying that a recent random sample of 300 fries was tested from a shipment and 27 fries had dark ends. Assuming that the population does meet the 0.06 standard, what is the probability of getting a sample of 300 with 27 or more dark ends? 0.0162 0.0231 0.0341 0.0012

0.0162

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean. What is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviations above the mean? 0.0024 0.0231 0.0512 0.0179

0.0179

United Manufacturing and Supply makes sprinkler valves for use in residential sprinkler systems. United supplies these valves to major companies such as Rain Bird and Nelson, who in turn sell sprinkler products to retailers. United recently entered into a contract to supply 40,000 sprinkler valves. The contract called for at least 97% of the valves to be free of defects. Before shipping the valves, United managers tested 200 randomly selected valves and found 190 defect-free valves in the sample. The managers wish to know the probability of finding 190 or fewer defect-free valves if in fact the population of 40,000 valves is 97% defect-free. The probability is: 0.0111 0.0212 0.0475 0.0612

0.0475

The National Association of Realtors released a survey indicating that a surprising 43% of first-time home buyers purchased their homes with no-money-down loans during 2005. The fear is that house prices will decline and leave homeowners owing more than their homes are worth. PMI Mortgage Insurance estimated that there existed a 50% risk that prices would decline within two years in major metro areas such as San Diego, Boston, Long Island, New York City, Los Angeles, and San Francisco. A survey taken by realtors in the San Francisco area found that 12 out of the 20 first-time home buyers sampled purchased their home with no-money-down loans. Calculate the probability that at least 12 in a sample of 20 first-time buyers would take out no-money-down loans if San Francisco's proportion is the same as the nationwide proportion of no-money-down loans. 0.0441 0.0124 0.0512 0.0618

0.0618

According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical, civil, and industrial) were women. Suppose a random sample of 50 engineers is selected. How likely is it that the random sample of 50 engineers will contain 8 or more women in these positions? 0.1612 0.1020 0.0314 0.0821

0.1020

A normally distributed population has a mean of 500 and a standard deviation of 60. Determine the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515. 0.0151 0.0712 0.1056 0.1761

0.1056

Suppose that a population is known to be normally distributed with mean = 2,000 and standard deviation = 230. If a random sample of size n = 8 is selected, calculate the probability that the sample mean will exceed 2,100. 0.1093 0.0712 0.1871 0.2141

0.1093

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours. What is the probability that a single battery randomly selected from the population will have a life between 70 and 80 hours? 0.3830 0.1712 0.5121 0.2412

0.3830

According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical, civil, and industrial) were women. Suppose a random sample of 50 engineers is selected. How likely is it that the random sample will contain fewer than 5 women in these positions? 0.5121 0.5512 0.3124 0.4522

0.4522

In a standard normal distribution, the probability that z is greater than 0 is: 1.96 equal to 1 0.5 at least 0.5

0.5

Given a population with size 500, in which the probability of success is p = 0.20, calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23 if the sample size is 200. 0.6165 0.7121 0.8911 0.8712

0.6165

For a standardized normal distribution, calculate P(-1.00 < z < 1.00). 0.6667 0.4572 0.6826 0.5521

0.6826

Consider a random variable, z, that has a standardized normal distribution. Determine P(z > -1). 0.1251 0.1512 0.8413 0.2124

0.8413

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours. If the manufacturer of the battery is able to reduce the standard deviation of battery life from 10 to 9 hours, what would be the probability that 16 batteries randomly sampled from the population will have a sample mean life of between 70 and 80 hours? 0.9736 0.8812 0.8124 0.6127

0.9736

Consider a random variable, z, that has a standardized normal distribution. Determine (-2 ≤ z ≤ 3). 0.47722 0.12414 0.49865 0.97587

0.97587

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean. What is the probability that a randomly selected value from the distribution will be less than 2.1 standard deviations from the mean? 0.9976 0.9821 0.9712 0.9488

0.9821

For a standardized normal distribution, determine a value, say z0, so that P(-z0 ≤ z ≤ z0) = 0.95. 1.24 1.96 1.65 2.14

1.96

For a standardized normal distribution, determine a value, say z0, so that P(z > z0) = 0.025. 1.65 1.24 2.14 1.96

1.96

In a recent report, it was stated that the proportion of employees who carpool to their work is 0.14 and that the standard deviation of the sampling proportion is 0.0259. However, the report did not indicate what the sample size was. What was the sample size? 180 460 100 Can't be determined without more information

180

A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution, what value will be exceeded 85% of the time? 19.8 17.9 16.2 14.2

19.8

A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution, determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it. 21.65 and 28.35 16.23 and 18.82 18.85 and 27.94 19.31 and 21.12

21.65 and 28.35

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? About 0.004 About 0.02 Approximately 0.1026 Approximately 0.2013

About 0.004

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. Based on this, what is the probability that a call will last longer than 13 minutes? About 0.0125 Approximately 0.4875 About 0.9875 About 0.5125

About 0.0125

A pharmaceutical company claims that only 5 percent of patients experience nausea when they take a particular drug. In a research study, n = 100 patients were given this drug and 8 experienced nausea. Assuming that the company's claim is true, what is the probability of 8 or more patients experiencing nausea? About 0.0300 About 0.9162 About 0.4162 About 0.0838

About 0.0838

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? About 654 minutes About 237 minutes About 390 minutes About 325 minutes

About 237 minutes

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. -0.133 pounds 1.144 pounds Approximately 0.05 pounds None of the above

Approximately 0.05 pounds

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? Approximately 0.29 About 0.48 About 0.68 Nearly 0.75

Approximately 0.29

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. Just over 2 pounds Nearly 1.27 pounds Approximately 2.33 pounds Approximately 1.86 pounds

Approximately 1.86 pounds

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? Approximately 2.34 mpg 1.8 mpg Approximately 3.1 mpg 0.77 mpg

Approximately 2.34 mpg