Question : A sociologist recently conducted a survey of senior citizens who have net worths too high : 2150376
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
40) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows:
Find the median of the observations.
A) 75
B) 71
C) 74
D) 74.5
41) The scores for a statistics test are as follows:
Compute the mean score.
A) 80.05
B) 76.85
C) 67.80
D) 75
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
43) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed:
Calculate the mean and median for the data.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
47) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 104 miles per hour. Suppose that the statistician indicated that the serve speed distribution was skewed to the left. Which of the following values is most likely the value of the median serve speed?
A) 88 mph
B) 104 mph
C) 112 mph
D) 96 mph
48) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the mean is correct?
A) The average of the textbook costs sampled was $500
B) 50% of the students sampled had textbook costs equal to $500
C) The most frequently occurring textbook cost in the sample was $500
D) 50% of the students sampled had textbook costs that were less than $500
49) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct?
A) The average of the textbook costs sampled was $425
B) 50% of the students sampled had textbook costs equal to $425
C) 50% of the students sampled had textbook costs that were less than $425
D) The most frequently occurring textbook cost in the sample was $425
50) During one recent year, U.S. consumers redeemed 6.31 billion manufacturers' coupons and saved themselves $2.56 billion. Calculate and interpret the mean savings per coupon.
A) The average savings was 246.5 cents per coupon.
B) Half of all coupons were worth more than $0.41 in savings.
C) The average savings was $0.41 per coupon.
D) Half of all coupons were worth more than 246.5 cents in savings.
51) The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5.
Interpret the year 5 median dropout rate of 25.43.
A) The most frequently observed dropout rate of the 51 states was 25.43%.
B) Most of the 51 states had a dropout rate close to 25.43%.
C) Half of the 51 states had a dropout rate below 25.43%.
D) Half of the 51 states had a dropout rate of 25.43%.
54) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean of the test scores is 79. Additional information indicated that the median of the test scores was 89. What type of distribution most likely describes the shape of the test scores?
A) unable to determine with the information given
B) skewed to the right
C) skewed to the left
D) symmetric
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
59) The output below displays the mean and median for the state high school dropout rates in year 1 and in year 5.
Use the information to determine the shape of the distributions of the high school dropout rates in year 1 and year 5.
60) The total points scored by a basketball team for each game during its last season have been summarized in the table below. Identify the modal class of the distribution of scores.
|
Score |
Frequency |
|
41-60 |
3 |
|
61-80 |
8 |
|
81-100 |
12 |
|
101-120 |
7 |
Solve the problem.
68) Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed:
Calculate the sample variance.
A) 406.877
B) 3905.772
C) 1936.283
D) 2160.733
69) Calculate the range of the following data set:
8, 9, 9, 2, 6, 13, 9, 7, 4
A) 2
B) 15
C) 13
D) 11
70) The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places.
200, 105, 100, 190, 160
A) 243.2745
B) 175.0528
C) 46.6905
D) 136.03
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
73) The ages of five randomly chosen professors are 42, 55, 45, 51, and 59. Calculate the sample variance of these ages.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
78) Compute s2 and s for the data set: -3, 1, -3, -3, 1, -3
A) 18.73; 4.33
B) 3.6; 1.9
C) 4.27; 2.07
D) 3; 1.73
79) Compute s2 and s for the data set: (4/5),(2/5), (4/5), (1/5), (3/5), (1/10).
A) 8.967; 2.994
B) 1.62; 1.273
C) 0.028; 0.167
D) 0.09; 0.299
101) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 104 miles per hour (mph) and the standard deviation of the serve speeds was 14 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player's serves was between 118 mph and 132 mph?
A) 0.1350
B) 132
C) 0.95
D) 0.270
103) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. The mean and the standard deviation for their responses were 18 and 5, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a symmetric, mound-shaped distribution. Give an interval where you believe approximately 95% of the television viewing times fell in the distribution.
A) less than 13 and more than 23 hours per week
B) less than 28
C) between 8 and 28 hours per week
D) between 3 and 33 hours per week
105) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 84 jobs and a standard deviation of 9. Where do we expect approximately 95% of the distribution to fall?
A) between 66 and 102 jobs per day
B) between 57 and 111 jobs per day
C) between 75 and 93 jobs per day
D) between 102 and 111 jobs per day
106) A study was designed to investigate the effects of two variables — (1) a student's level of mathematical anxiety and (2) teaching method — on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 490 with a standard deviation of 20 on a standardized test. Assuming a mound-shaped and symmetric distribution, what percentage of scores exceeded 450?
A) approximately 97.5%
B) approximately 100%
C) approximately 95%
D) approximately 84%
107) A study was designed to investigate the effects of two variables — (1) a student's level of mathematical anxiety and (2) teaching method — on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 370 with a standard deviation of 50 on a standardized test. Assuming a mound-shaped and symmetric distribution, in what range would approximately 95% of the students score?
A) between 270 and 470
B) above 470
C) below 270 and above 470
D) below 470
108) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $92 and a standard deviation of $13. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $79?
A) approximately 84%
B) approximately 34%
C) approximately 95%
D) approximately 16%
109) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 80 and 5, respectively, and the distribution of scores is mound-shaped and symmetric. What percentage of test-takers scored better than a trainee who scored 65?
A) approximately 84%
B) approximately 100%
C) approximately 97.5%
D) approximately 95%
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
110) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 104 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. Find the percentage of serves that were hit faster than 59 mph.
111) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 84 jobs and a standard deviation of 6. On what percentage of days do the number of jobs submitted exceed 90?
112) By law, a box of cereal labeled as containing 24 ounces must contain at least 24 ounces of cereal. The machine filling the boxes produces a distribution of fill weights that is mound-shaped and symmetric, with a mean equal to the setting on the machine and with a standard deviation equal to 0.04 ounce. To ensure that most of the boxes contain at least 24 ounces, the machine is set so that the mean fill per box is 24.12 ounces. What percentage of the boxes do, in fact, contain at least 24 ounces?
113) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 76 and 2, respectively, and the distribution of scores is mound-shaped and symmetric. If a firm wanted to give the best 2.5% of the trainees a big promotion, what test score would be used to identify the trainees in question?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
115) The distribution of scores on a test is mound-shaped and symmetric with a mean score of 78. If 68% of the scores fall between 72 and 84, which of the following is most likely to be the standard deviation of the distribution?
A) 3
B) 2
C) 6
D) 12
117) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 8 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves.
A) 84 mph to 116 mph
B) 68 mph to 132 mph
C) 76 mph to 124 mph
D) 124 mph to 148 mph
119) By law, a box of cereal labeled as containing 20 ounces must contain at least 20 ounces of cereal. The machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.02 ounce. To ensure that most of the boxes contain at least 20 ounces, the machine is set so that the mean fill per box is 20.06 ounces. Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 20 ounces.
A) The proportion is less than 2.5%.
B) The proportion is at most 5.5%.
C) The proportion is at least 89%.
D) The proportion is at most 11%.
120) A study was designed to investigate the effects of two variables — (1) a student's level of mathematical anxiety and (2) teaching method — on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 310 with a standard deviation of 20 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 270 and 350?
A) at least 89%
B) approximately 95%
C) at least 75%
D) approximately 68%
121) A study was designed to investigate the effects of two variables — (1) a student's level of mathematical anxiety and (2) teaching method — on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 490 with a standard deviation of 40 on a standardized test. Assuming a non-mound-shaped distribution, what percentage of the students scored over 610?
A) at least 89%
B) at most 11%
C) approximately 2.5%
D) at most 5.5%
122) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $110 and a standard deviation of $10. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $90?
A) at most 25%
B) at most 11.1%
C) at least 88.9%
D) at least 75%
123) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 83 and 3, respectively. Assuming nothing is known about the distribution, what percentage of test-takers scored above 89?
A) approximately 97.5%
B) at most 25%
C) at least 75%
D) approximately 2.5%
124) If nothing is known about the shape of a distribution, what percentage of the observations fall within 3 standard deviations of the mean?
A) approximately 99.7%
B) at most 11%
C) at least 89%
D) approximately 0.3%
Solve the problem.
132) Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 75 and 3, respectively, and the distribution of scores is mound-shaped and symmetric. Suppose the trainee in question received a score of 71. Compute the trainee's z-score.
A) z = -12
B) z = 0.91
C) z = -4
D) z = -1.33
134) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $113 and a standard deviation of $11. Three solar homes reported monthly utility bills of $73, $76, and $72. Which of the following statements is true?
A) Homes using solar power may actually have higher utility bills than homes using only gas and electricity.
B) Homes using solar power may have lower utility bills than homes using only gas and electricity.
C) Homes using solar power always have lower utility bills than homes using only gas and electricity.
D) The utility bills for homes using solar power are about the same as those for homes using only gas and electricity.
135) A radio station claims that the amount of advertising each hour has a mean of 17 minutes and a standard deviation of 2.1 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 13 minutes. Calculate the z-score for this amount of advertising time.
A) z = 0.64
B) z = 1.90
C) z = -8.4
D) z = -1.90
136) On a given day, the price of a gallon of milk had a mean price of $2.71 with a standard deviation of $0.05. A particular food store sold milk for $2.6/gallon Interpret the z-score for this gas station.
A) The milk price of this food store falls 5 standard deviations above the mean milk price of all food stores.
B) The milk price of this food store falls 1 standard deviation below the milk gas price of all food stores.
C) The milk price of this food store falls 1 standard deviation above the mean milk price of all food stores.
D) The milk price of this food store falls 5 standard deviations below the mean milk price of all food stores.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
138) A study was designed to investigate the effects of two variables — (1) a student's level of mathematical anxiety and (2) teaching method — on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 320 and a standard deviation of 20 on a standardized test. Find and interpret the z-score of a student who scored 500 on the standardized test.
139) A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $118.00 and a standard deviation of $14.00 Assuming the distribution is mound-shaped and symmetric, would you expect to see a 3-bedroom house using gas or electric energy with a monthly utility bill of $202.00? Explain.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
140) Find the z-score for the value 74, when the mean is 58 and the standard deviation is 2.
A) z = 7.50
B) z = -1.24
C) z = 1.24
D) z = 8.00
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
141) Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a mean of 69 with a standard deviation of 3.7. One student earned a 55 on the history test and a 66 on the physics test. Calculate the z-score for each test. On which test did the student perform better?
Solve the problem.
148) When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 98th percentile on the verbal part of the test and at the 14th percentile on the quantitative part. Interpret these results.
A) This student performed better than 98% of the other test-takers on the verbal part and better than 
on the quantitative part.
B) This student performed better than 2% of the other test-takers on the verbal part and better than 
on the quantitative part.
C) This student performed better than 98% of the other test-takers on the verbal part and better than 
on the quantitative part.
D) This student performed better than 2% of the other test-takers on the verbal part and better than 
on the quantitative part.
150) Summary information is given for the weights (in pounds) of 1000 randomly sampled tractor trailers.
Find the percentage of tractor trailers with weights between 5608 and 8608 pounds.
A) 75%
B) 50%
C) 100%
D) 25%
Solve the problem.
157) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 98 miles per hour (mph) and the standard deviation of the serve speeds was 14 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds?
Speeds: 49 mph, 112 mph, and 126 mph
A) 49, 112, and 126 are all outliers.
B) 49 and 112 are both outliers, but 126 is not.
C) 49 is the only outlier.
D) None of the three speeds is an outlier.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
162) A radio station claims that the amount of advertising each hour has an a mean of 16 minutes and a standard deviation of 2.2 minutes. You listen to the radio station for 1 hour and observe that the amount of advertising time is 10.72 minutes. Based on your observation, what would you infer about the radio station's claim?
Solve the problem.
170) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The lower quartile of a particular player's serve speeds was reported to be 97 mph. Which of the following interpretations of this information is correct?
A) 75% of the player's serves were hit at speeds less than 97 mph.
B) 25% of the player's serves were hit at 97 mph.
C) 75% of the player's serves were hit at speeds greater than 97 mph.
D) 97 serves traveled faster than the lower quartile.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
172) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). Three hundred parents of elementary school-aged children were asked to estimate the number of hours per week that their child watches television. The upper quartile for the distribution was given as 14 hours. Interpret this value.
