Name Date Period. E) Lowest score: 67, mean: 104, median: 112, range: 83, IQR: 102, Q1: 46, SD: 17

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1 Chapter 6 Review Standards: 4, 7, 8, and 11 Name Date Period Write complete answers, using complete sentences where necessary. Show your work when possible. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use summary statistics to answer the question. 1) Here are some summary statistics for the recent English exam: lowest score = 34, mean score = 74, median = 88.2, range = 76, IQR = 59, Q1= 30, standard deviation = 8.6. Is the distribution symmetric, skewed to the left, or skewed to the right? Explain. A) Skewed to the left, mean lower than median. B) Symmetric, mean lower than median. C) Skewed to the right, mean higher than median. D) Skewed to the right, mean lower than median. E) Skewed to the left, mean higher than median. 1) 2) The speed vehicles travelled on a local highway was recorded for one month. The speeds ranged from 50 mph to 68 mph with a mean speed of 54 mph and a standard deviation of 8 mph. The quartiles and median speeds were 56 mph, 65 mph, and 53 mph. Is the distribution symmetric, skewed to the left, or skewed to the right? Explain. A) Skewed to the right, mean lower than median. B) Symmetric, mean higher than median. C) Skewed to the left, mean lower than median. D) Skewed to the left, mean higher than median. E) Skewed to the right, mean higher than median. 2) 3) Consider a data set of positive values, at least two of which are not equal. Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1? 3) I. The mean II. The median III. The standard deviation A) I only B) II only C) III only D) I and II only E) I, II, and III Use summary statistics to answer the question. 4) Here are some statistics for the annual Wildcat golf tournament: lowest score = 60, mean score = 97, median = 105, range = 90, IQR = 102, Q1 = 39 standard deviation = 17. Suppose it was very windy and all the golfers' scores went up by 7 strokes. Tell the new value for each of the summary statistics. A) Lowest score: 67, mean: 104, median: 112, range: 90, IQR: 102, Q1: 46, SD: 17 B) Lowest score: 67, mean: 104, median: 112, range: 83, IQR: 102, Q1: 46, SD: 24 C) Lowest score: 67, mean: 104, median: 112, range: 83, IQR: 109, Q1: 46, SD: 17 D) Lowest score: 67, mean: 97, median: 105, range: 83, IQR: 102, Q1: 46, SD: 17 E) Lowest score: 67, mean: 104, median: 112, range: 83, IQR: 102, Q1: 46, SD: 17 4) 1

2 5) The speed vehicles traveled on a local highway was recorded for one month. The speeds ranged from 49 mph to 64 mph with a mean speed of 55 mph and a standard deviation of 8 mph. The quartiles and median speeds were 52 mph, 61 mph, and 52 mph. Suppose increased patrols reduced speeds by 7%. Find the new mean and standard deviation. Express your answer in exact decimals. A) Mean: mph, SD: 8 mph B) Mean: 3.85 mph, SD: 0.56 mph C) Mean: mph, SD: 8 mph D) Mean: mph, SD: 8.56 mph E) Mean: mph, SD: 7.44 mph 5) 6) Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $30,000, mean salary = $70,000, median = $50,000, range = $120,000, IQR = $60,000, first quartile = $35,000, standard deviation = $40,000. 6) Between what two values are the middle 50% of the salaries found? A) $35,000 and $75,000 B) $30,000 and $150,000 C) $35,000 and $95,000 D) $70,000 and $50,000 E) $35,000 and $60,000 7) Here are some summary statistics for all of the runners in a local 12K race: slowest time =20 minutes, mean = 70 minutes, median = 84 minutes, range = 101 minutes, IQR = 64, Q1 = 34, standard deviation = 10 minutes. Between what two values are the middle 50% of times? A) 16.8 and 67.2 B) 42 and 84 C) 21 and 63 D) 34 and 98 E) 131 and 30 7) Find the number of standard deviations from the mean. Round to the nearest hundredths. 8) A town's average snowfall is 33 inches per year with a standard deviation of 11 inches. How many standard deviations from the mean is a snowfall of 66 inches? A) About 3.00 standard deviations below the mean B) About 0.33 standard deviations below the mean C) About 0.33 standard deviations above the mean D) About 3.00 standard deviations above the mean E) About 2.00 standard deviations above the mean 8) 9) The weights of children age two average 25 pounds with a standard deviation of 4 pounds. How many standard deviations from the mean is a weight of 14 pounds? A) About 1.79 standard deviations above the mean B) About 2.75 standard deviations above the mean C) About 1.50 standard deviations below the mean D) About 2.75 standard deviations below the mean E) About 1.50 standard deviations above the mean 9) 2

3 Solve the problem. 10) A town's snowfall in December averages 13 inches with a standard deviation of 8 inches while in February, the average snowfall is 40 inches with a standard deviation of 13 inches. In which month is it more likely to snow 32 inches? Explain. A) February. Snowfall of 32 inches is 19 8 from the mean while snowfall of 32 inches is from the mean in December. B) It is equally likely in either month. One can't predict Mother Nature. C) February. Snowfall of 32 inches is from the mean in December. D) December. Snowfall of 32 inches is from the mean in February. from the mean while snowfall of 32 inches is 19 8 from the mean while snowfall of 32 inches is 19 8 E) December. Snowfall of 32 inches is 19 8 from the mean while snowfall of 32 inches is from the mean in February. 10) 11) The mean weights for medium navel oranges is 9.8 ounces. Suppose that the standard deviation for the oranges is 3.3 ounces. Which would be more likely, an orange weighing 14 ounces or an orange weighing 4.9 ounces? Explain. A) A 4.9 ounce orange is more likely (z = -1.48) compared with an orange weighing 14 ounces (z = 1.27). B) A 4.9 ounce orange is more likely (z = 1.27) compared with an orange weighing 14 ounces (z = -1.48). C) A 14 ounce orange is more likely (z = 1.27) compared with an orange weighing 4.9 ounces (z = -1.48). D) A 14 ounce orange is more likely (z = -1.48) compared with an orange weighing 4.9 ounces (z = 1.27). E) A 4.9 ounce orange is more likely (z = 1.48) compared with an orange weighing 14 ounces (z = 4.24). 11) Pick the appropriate standard deviation. 12) You heard that the average number of years of experience among stockbrokers is 15 years. You can't remember the standard deviation. Find an appropriate standard deviation. A) 3 months B) 6 months C) 9 months D) 3 years E) 9 years 12) 13) The average score on the Chapter 4 mathematics test was 60 points (out of 100 points). Find an appropriate standard deviation. A) 3 points B) 1 point C) 16 points D) 20 points E) 8 points 13) 3

4 Draw the Normal model and use the Rule to answer the question. 14) Assuming a Normal model applies, a town's average annual snowfall (in inches) is modeled by N(48, 7). Draw and label the Normal model. What percent of snowfall is between 27 inches and 55 inches? A) 14) B) Snowfall (in.) ; 99.7% C) Snowfall (in.) ; 68% D) Snowfall (in.) ; 83.85% E) Snowfall (in.) ; 52.15% Snowfall (in.) ; 36.3% SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 15) The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz? 15) 4

5 16) A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, what percentage can be expected to be between 200 and 275? 16) 17) The lengths of human pregnancies can be described by a Normal model with a mean of 268 days and a standard deviation of 15 days. What percentage can we expect for a pregnancy that will last at least 300 days? 17) 18) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores over 85. Round to the nearest tenth of a percent. 18) In a standard Normal model, state what value(s) of z cuts off the described region. Solve with and without a calculator. 19) the lowest 96% 19) 20) the highest 7% 20) 21) the middle 87.4% 21) 22) the lowest 4% 22) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the percent of a standard Normal model found in the given region with and without a calculator. Round to the nearest hundredth of a percent. 23) 0 < z < ) A) 43.67% B) 49.87% C) 50.13% D) 99.87% E) 12.17% 24) z < ) A) 12.92% B) 88.09% C) 89.07% D) 87.08% E) 84.85% 25) z > ) A) 72.24% B) 27.76% C) 25.47% D) 22.24% E) 21.90% 5

6 26) < z < ) A) 22.11% B) % C) 48.84% D) 75.57% E) 76.47% 27) z > ) A) -3.44% B) 3.44% C) 46.56% D) 96.56% E) 92.57% Solve the problem with and without a calculator. Round to the nearest tenth. 28) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the 30th percentile. A) 61.2 B) 68.2 C) 77.8 D) 63.8 E) ) 29) Based on the Normal model for snowfall in a certain town N(57, 8), how many inches of snow would represent the 25th percentile? A) 51.6 inches B) 49 inches C) 65 inches D) 14.3 inches E) 62.4 inches 29) 30) Based on the Normal model for car speeds on an old town highway N(77, 9.1), what is the cutoff value for the highest 15% of the speeds? A) about 11.6 mph B) about 63.1 mph C) about 86.5 mph D) about 65.5 mph E) about 67.5 mph 30) 31) Based on the Normal model for car speeds on an old town highway N(77, 9.1), what are the cutoff values for the middle 20% of the speeds? A) about 74.7 mph, about 79.3 mph B) about 84.7 mph, about 69.3 mph C) about 95.2 mph, about 58.8 mph D) about 61.6 mph, about 92.4 mph E) about 86.1 mph, about 67.9 mph 31) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the missing parameter. 32) µ = 60.0, 4.01% below 53; =? 32) 33) = 0.01, 2.28% below 0.32; µ =? 33) 6

7 34) µ = 0.38, 20% above 0.50; =? 34) 35) = 20, 48% above 150; µ =? 35) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round to the nearest hundredth. 36) After increased patrol, cars on an old town highway travel at speeds averaging 53 mph. If 93% of vehicles travel below 68 mph, what approximate standard deviation could represent this model (assuming a Normal model is appropriate)? A) B) C) D) E) ) 37) After increased patrol, 91% of vehicles on an old town highway travel above 45 mph with a standard deviation of 5.8. Assuming a Normal model is appropriate, find the mean speed. A) mph B) 50.8 mph C) mph D) 5.28 mph E) mph 37) Solve the problem. 38) The scores for a recent English exam can be represented by the Normal model N(66, 7.4). What score would you expect to be unusually low for this exam? A) 58.6 B) 62.3 C) 73.4 D) 43.8 E) ) 39) Here are the weekly winnings for several local poker players: $100, $50, $125, $75, $80, $60, $110, $150, $300, $700, $115, $75, $1000, $5000. Which is a better summary of the spread, the standard deviation or the IQR? Explain. A) IQR, the distribution is symmetric B) SD, the distribution is skewed C) Either, the distribution is symmetric D) SD, the distribution is symmetric E) IQR, the distribution is skewed 39) Provide an appropriate response. 40) Which of the following variables would most likely follow a Normal model? 40) A) heights of singers in a co-ed choir B) scores on an easy test C) weights of adult male elephants D) family income E) all of these 7

8 41) Suppose a Normal model describes the number of pages printer ink cartridges last. If we keep track of printed pages for the 47 printers at a company's office, which must be true? I. The page counts for those ink cartridges will be normally distributed. II. The histogram for those page counts will be symmetric. III. 95% of those page counts will be within 2 standard deviations of the mean. A) none B) I, II, and III C) II only D) I only E) II and III 41) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 42) You learn that your company is sending you and several other employees to staff a new office in China. While there everyone will earn the equivalent of their current salary, converted to Chinese currency at the rate of 8 yuans per dollar. In addition, everyone will earn a weekly foreign living allowance of 200 yuans. For example, since you are earning $1000 per week, your weekly salary in China will be 1000(8) = 8200 yuans. Shown are some summary statistics describing the current salaries of this group being sent overseas. Fill in the table to show what these statistics will be for the salaries you all will earn while in China. 42) Statistic In the US In China Minimum salary $400 Standard deviation $250 Median $750 IQR $300 8