Percentage of scores less than 70
> IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample. a. If the sample size is n = 64, find
> If we record the means from 1000 rolls of 100 dice, the resulting distribution will be closer to a normal distribution than if we record the means from 1000 rolls of 10 dice.
> For the samples described in Exercise 6, the sample means will vary less than the original incomes.
> The distribution of incomes of adults is a right- skewed distribution. Therefore, if we select many samples of 64 incomes at random from this distribution, the means of these samples will also have a right-skewed distribution.
> The Journal of the American Medical Association prints an article evaluating a drug, and some of the physicians who wrote the article received funding from the pharmaceutical company that produces the drug.
> A process consists of repeating this operation: Randomly select two values from a normally distributed population and then find the mean of the two values. The sample means will be normally distributed, even though each sample has only two values.
> Briefly explain a major reason why the Central Limit Theorem is useful in statistics.
> What is the Central Limit Theorem? When does it apply?
> My professor graded the final on a curve, and she gave a grade of A+ to anyone who had a standard score of 2 or more.
> What is a percentile? Describe how Table A-1 (in Appendix A) allows you to relate standard scores and percentiles.
> Are there broad regions where melanoma mortality is more common than others? Which ones, and what do they have in common? Figure 3.26
> What is a standard score? How do you find the standard score for a particular data value?
> For a normal distribution, approximately what fraction of data values lie more than 1 standard deviation above the mean? When might data values be considered unusual? Explain.
> What is the 68-95-99.7 rule for normal distributions? Does it apply to other (not normal) distributions as well?
> Based on a random sample of movie lengths, the mean length is 110.5 minutes with a standard deviation of 22.4 minutes. Assume that movie lengths are normally distributed. a. What percentage of movies are more than 2 hours long? b. What percentage of movi
> Heights of adult American males are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that males have heights between 64 inches and 78 inches. What percentages of males are eligible for
> Monsanto hires independent university scientists to determine whether its new, GMO (genetically modified organism) soybean poses any threat to consumers.
> At the district spelling bee, the girls have normally distributed scores with a mean score of 71 points and a standard deviation of 6 those students with a score greater than 75 are eligible to go to the state spelling bee. What percentage of the girls w
> Assume that body temperatures of healthy adults are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. a. What percentage of adults have body temperatures greater than 99.99°F? b. What percentage of adults have body temperatu
> Assume that the scores on the Graduate Record Exam (GRE) are normally distributed with a mean of 497 and a standard deviation of 115. a. A graduate school requires a GRE score of 650 for admission. To what percentile does this correspond? b. A graduate
> Based on data from the College Board, SAT scores on the Math Level 1 test are normally distributed with a mean of 621 and a standard deviation of 96. a. Find the percentage of scores greater than 600. b. Find the percentage of scores less than 700. c.
> The stack plot in Figure 3.25 shows the numbers of bachelor’s degrees awarded to males and females since 1970. The last few years are projections. a. Estimate the numbers of bachelor’s degrees to be awarded to males an
> Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. What percentage of pregnancies last less than 250 days? b. What percentage of pregnancies last more than 300 days? c. If a birth is considered
> Consider the following table, showing the official mean weight and estimated standard deviation for five U.S coins. Suppose a vending machine is designed to reject all coins with weights more than 2 standard deviations above or below the mean. For each c
> The percentage of heights between 150 cm and 170 cm
> The percentage of heights between 180 cm and 200 cm
> The percentage of heights between 160 cm and 188 cm
> The percentage of heights between 167 cm and 181 cm
> Consumer Reports magazine prints a review of new cars and does not accept free products or run any advertisements from any companies.
> The percentage of heights greater than 180 cm
> The percentage of heights less than 146 cm
> The percentage of heights less than 200 cm
> The stack plot in Figure 3.24 on the next page shows Congressional Budget Office data for actual spending (through 2011) and projected spending on federal entitlement programs through 2085 as percentages of the gross domestic product (GDP). Interpret the
> The percentage of heights less than 160 cm
> The percentage of heights greater than 167 cm
> The percentage of heights greater than 181 cm
> The percentage of heights less than 181 cm
> The percentage of heights greater than 174 cm
> Percentage of scores between 88 and 127
> Percentage of scores between 70 and 115
> A pollster for the U.S. Department of Labor surveys 1500 randomly selected adults about their employment status.
> Percentage of scores between 70 and 130
> Percentage of scores between 85 and 115
> The graph in Figure 3.23 depicts U.S. marriage and divorce rates for selected years. The marriage rates are depicted by the blue bars, and the divorce rates are depicted by the maroon bars. The rates are given as number of marriages or divorces per 1000
> Percentage of scores greater than 145
> Percentage of scores greater than 88
> Percentage of scores less than 91
> Percentage of scores less than 130
> Percentage of scores greater than 70
> Percentage of scores less than 115
> Percentage of scores greater than 100
> You want to conduct a survey to determine the proportion of eligible voters in California likely to vote for the Democratic presidential candidate in the next election. • Sample 1: All eligible voters in San Diego County • Sample 2: All eligible voters
> Adult males have sitting knee heights that are normally distributed with a mean of 21.4 inches and a standard deviation of 1.2 inches. Use the 68-95-99.7 rule to find the indicated quantity. a. Find the percentage of adult males with sitting knee height
> Consider the display in Figure 3.22 of median salaries of males and females in recent years. a. What general trends does the graph convey? b. Redraw the graph as a multiple line graph (with two lines). Briefly discuss the advantages and disadvantages of
> In a study of facial behavior, people in a control group are timed as to the duration of eye contact they make in a 5-minute period. Their times are normally distributed with a mean of 184.0 seconds and a standard deviation of 55.0 seconds (based on data
> Pulse rates for adult females are normally distributed with a mean of 74.0 beats per minute (bpm) and a standard deviation of 12.5 bpm. Use the 68-95-99.7 rule to find the following values. a. Percentage of pulse rates less than 74 bpm b. Percentage of p
> A test of depth perception is designed so that scores are normally distributed with a mean of 50 and a standard deviation of 10. Use the 68-95-99.7 rule to find the following values. a. Percentage of scores less than 50 b. Percentage of scores less than
> I found the standard score of the data value, even though I do not know the standard deviation of the data set.
> My good grades are a result of the fact that the number of hours I study each week put me in the 90th percentile for study time.
> My height puts me in the 37th percentile for my gender, which means my height has a negative standard score.
> Briefly describe the four conditions under which we can expect a data set to have a nearly normal distribution. Give an example of a set of data that might be approximated by the normal distribution.
> What does the area under the normal distribution curve represent? What is the total area under the normal distribution curve?
> Draw a rough sketch of a normal distribution. Do all normal distributions look the same?
> You want to determine the average (mean) number of robocalls received each day by adults in Alaska. • Sample 1: The 537 adults in Alaska who respond to a survey published in a newspaper • Sample 2: The first 537 people to visit a particular Anchorage
> The graph in Figure 3.21 shows home prices in different regions of the United States. a. Describe general trends that apply to the home price data for all regions. b. Describe any differences that you notice among the different regions. Figure 3.21
> When we refer to a “normal” distribution, does the word normal have the same meaning as it does in ordinary usage? Explain.
> Consider the graph of the normal distribution in Figure 5.15, which gives the relative frequencies in a distribution of body weights for a sample of male students. a. What is the mean of the distribution? b. Estimate (using area) the percentage of studen
> Consider the graph of the normal distribution in Figure 5.14, which illustrates the relative frequencies in a distribution of systolic blood pressures (in standard units of millimeters of mercury) for a sample of female students. The distribution has a s
> Consider the graph of the normal distribution in Figure 5.13, which shows the relative frequencies in a distribution of IQ scores. The distribution has a mean of 100 and a standard deviation of 16. a. What is the total area under the curve? b. Estimate (
> Consider the graph of the normal distribution in Figure 5.12, which gives relative frequencies in a distribution of men’s heights. The distribution has a mean of 69.6 inches and a standard deviation of 2.8 inches. a. What is the total a
> Figure 5.11 shows a histogram for the weights (in grams) of 100 randomly selected M&M plain candies. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not? Figure 5.11
> Figure 5.10 on the next page shows a histogram for the departure delay times (in minutes) of 152 American Airlines flights from Los Angeles to San Francisco. Is this distribution close to normal? Should this variable have a normal distribution? Why or wh
> The amount of nicotine absorbed by the human body can be determined by measuring the amount of cotinine (ng/ml) in the blood. Figure 5.9 shows a histogram for the amounts of cotinine measured in 40 adults who do not smoke but are exposed to second-hand s
> Figure 5.8 shows a histogram for the body temperatures (in °F) of 500 randomly selected adults. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not? Figure 5.8
> The amounts of income tax paid by 5000 randomly selected U.S. adults.
> The stack plot in Figure 3.20 shows the numbers of higher education students enrolled in public and private colleges. The last few bars are projections from the U.S. National Center for Education Statistics. a. Describe any trends revealed on this graphi
> In a Gallup poll of 1059 randomly selected adults, 39% answered “yes” when asked “Do you have a gun in your home?”
> The departure delay times (in minutes past the scheduled time) of Amtrak trains leaving New York City for Boston.
> The outcomes of many tosses of a single die with 12 sides numbered 1 through 12.
> The measured systolic blood pressure of randomly selected adult males.
> The measured voltage amounts from newly manufactured AAA batteries made by Duracell.
> The pulse rates of randomly selected adult females.
> The winning numbers drawn in California’s Daily Four lottery game, in which four digits between 0 and 9 are drawn and digits can be repeated.
> The amounts of rainfall (in inches) on each day of a year in Boston.
> Identify the distribution in Figure 5.7 that is not normal. Of the two normal distributions, which has the larger standard deviation? Figure 5.7
> Identify the distribution in Figure 5.6 that is not normal. Of the two normal distributions, which has the larger standard deviation? Figure 5.6
> Every 100th iPhone screen is tested for readability
> Refer to the QWERTY data in Exercise 21 in Section 3.1 and construct a dot plot.
> The distribution of annual incomes of U.S. adults is a normal distribution.
> A pollster conducts a research project about how adult Americans pay their bills. She posts her survey on a website and obtains 47 responses.
> The distribution of the weights of all adult elephants in Kenya is a normal distribution.
> The distribution of Chrome book sales data over the last year is not normal, because it has two modes corresponding to the holiday season and back-to-school season.
> Among a sample of 1037 adult women, pulse rates are normally distributed with a mean of 74.0 beats per minute, but 75% of the women have pulse rates greater than 74.0 beats per minute.
> A manufacturer uses two different production sites to make batteries for cell phones. There is a defect rate of 2% at one of the sites and a defect rate of 4% at the other site. Therefore, the overall rate of defects must be 3%.
> Siena wins each of the first two sets of a tennis tournament by winning more games than her opponent in the first set and also winning more games than her opponent in the second set. It follows that Siena won more games than her opponent overall in the f
> When the Giants and Patriots football teams play each other, is it possible for one of the quarterbacks to have a higher passing percentage in each half while having a lower passing percentage for the entire game?
> If you are pulled over while driving and given a breathalyzer test for alcohol, what is the result called if the test incorrectly indicates that you have consumed alcohol?
> A professional soccer player is given a test for a banned substance. What does it mean when she is told that the result is positive? Do we know from such a positive result whether the player actually used the banned substance?
> When constructing a histogram of blood platelet counts, it is better to use three-dimensional bars in the graph.
> Professional athletes are routinely barred from participation for using banned substances. For such a test, what is a false positive? What is a false negative? What is a true positive? What is a true negative?
