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Practice exam 0.Suppose that the efficacy of a certain drug is 0.48. Consider the sampling distribution (sample size n = 160) for the proportion of patients cured by this drug. What is the mean of this distribution? What is the standard deviation of this distribution? (Round answer to four decimal places) 1. The following is the average daily temperature for Frederick, Maryland for the month of June: 78 93 77 75 74 89 90 81 73 86 79 86 84 80 90 87 79 87 73 79 74 84 90 85 77 70 72 85 85 87 (a) Complete the frequency distribution for the data. Age Frequency Relative Frequency 70-74 75-79 80-84 85-89 90-94 2. Consider the data set summarized by the following frequency distribution. x Frequency 15 6 16 4 17 7 18 9 19 12 20 17 21 8 22 4 (a) Find the mean of this data set. (b) Find the median of this data set. 3.The following data represents the age of 30 lottery winners. Given the frequency distribution for the data, Age Frequency Relative Frequency Cumulative Relative Frequency [20,29] 2 0.0667 0.0667 [30,39] 7 0.2333 0.3 [40,49] 8 0.2667 0.5667 [50,59] 7 0.2333 0.8 [60,69] 4 0.1333 0.9333 [70,79] 1 0.0333 0.9666 [80,89] 1 0.0333 0.9999 What is the frequency of lottery winners of age between 19 and 40? What percentage of lottery winners are 70 years or older? % What is the relative frequency of ages under 40? What is the cumulative relative frequency of lottery winners younger than 50? 4.The Inter-Quartile Range is obtained from subtracting the Incorrect quartile from the Incorrect quartile. 5.Find the 5 number summary for the data shown 2 10 30 38 41 45 46 48 62 73 78 87 92 94 5 number summary: , , , , IQRIQR: The 1.5XIQR1.5XIQR rule states that values between and are likely not outliers. 6. The five number summary of a dataset was found to be: 0, 2, 3, 13, 20 An observation is considered an outlier if it is below: An observation is considered an outlier if it is above: 7. Given the following set of data: 376 615 971 954 667 113 886 218 124 673 233 755 Determine the following: First quartile = Third quartile = IQR = 8. A sample was done, collecting the data below. Calculate the standard deviation, to one decimal place. x 30 5 22 15 10 9. Fill in the blanks. In a normal distribution, percent of the data are above the mean, and percent of the data are below the mean. Similarly, percent of all data points are within 1 standard deviation of the mean, percent of all data points are within 2 standard deviations of the mean, and percent are within 3 standard deviations of the mean. 10. Fill in the blanks. The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.25 inches. What value is one standard deviation below the mean? inches What value is one standard deviation above the mean? inches What is the probability that a randomly chosen location will have a snow depth between 2.25 and 2.75 inches? percent 11. The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1400 and the standard deviation is $120. What is the approximate percentage of buyers who paid between $1280 and $1520? % What is the approximate percentage of buyers who paid between $1400 and $1520? % What is the approximate percentage of buyers who paid between $1400 and $1760? % What is the approximate percentage of buyers who paid between $1160 and $1400? % What is the approximate percentage of buyers who paid less than $1160? % What is the approximate percentage of buyers who paid more than $1760? % 12. The annual rainfall in a certain region is approximately normally distributed with mean 42.8 inches and standard deviation 5.7 inches. Round answers to the nearest tenth of a percent. a) What percentage of years will have an annual rainfall of less than 44 inches? % b) What percentage of years will have an annual rainfall of more than 40 inches? % c) What percentage of years will have an annual rainfall of between 38 inches and 43 inches? % 13. A set of exam scores is normally distributed with a mean = 72 and standard deviation = 5. Use the Empirical Rule to complete the following sentences. 68% of the scores are between and . 95% of the scores are between and . 99.7% of the scores are between and . 14. A library checks out an average of 310 books per day with a standard deviation of 73 books. The number of books checked out follows an unknown distribution. Consider a random sample of 111 days of operation. Let ¯¯¯X=X¯=the average number of books checked out per day over a selection of 111 days. ¯¯¯X˜X¯~( , ) 15. A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-0.787 b=30.338 r2=0.364816 r=-0.604 Use this to predict the number of situps a person who watches 12.5 hours of TV can do (to one decimal place) 16. Let YY represent the profit (or loss) for a certain company XX years after 1980. Based on the data shown below, a statistician calculates a linear model Y=−0.44X+8.55Y x y 1 8.26 2 8.84 3 6.02 4 6.3 5 6.38 6 5.56 7 6.24 8 4.62 9 4.9 Use the model to estimate the profit in `1985 y = 17. A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=a+bx b=-0.665 a=23.079 r2=0.473344 r=-0.688 Use this to predict the number of situps a person who watches 3 hours of TV can do. Round to one decimal place. 18.