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STATISTICS PRACTICE TEST 2 1. Match the following. ____________ a. s A. (x x)2 ____________ b. ____________ c. range 4 B. n 1 n Cr Locator Value in a data set n! (n r )! r ! range rule of thumb for standard dev C. Standard dev for a sample ____________ d. xx s D. ____________ e. s 100 % x E. Coefficient of Variation _____________ f. L k n 100 Combinations Rule F. z score 2. To find rough estimates of the minimum and maximum “usual” values, give the formulas you could use; a. minimum “usual” value ________________________________ b. maximum “usual” value ________________________________ 3. One rule in interpreting values for a standard devation is the empirical rule. This rule states that for data sets, the following properties apply: About ______% of all values fall within 1 standard deviations of the mean. About ______% of all values fall within 2 standard deviations of the mean. About ______ % of all values fall withing 3 standard deviation of the mean. 4. Which of the following values is not needed to complete a Box Plot. _____________ Median Mean Q1 Minimum Q3 The owner of a small manufacturing plant employs six people. As part of their personnel file, they each gave the distance they travel to work, to the nearest tenth of a mile. The six distances are: 2.6 5.5 1.6 6.8 3.6 4.1 Find the following values. _________________ 5. Range _________________ 6. Standard Deviation – Use both formulas ( Show work below) Distances 7. The mean height of a basketball team is 6.1 feet with a standard deviation of .2 feet. The team’s center is 6.7 feet tall. Find the centers z score. Is his score unusual? _____________________ 7a. z score _____________________ b. Is it unusual? ____________________ 8. In a normal distribution, a set of scores has a mean of 22 and a standard deviation of 7. What percent of the scores fall between 1 and 43? 9. Given that the mean of a group of data is 15 and the standard deviation is 4: 9a. What percent of the population scored above 19? 9b. What percent of the population scored below 11? 9c. What percent of the population scored below 23? 9d. What percent of the population scored between 7 and 19? 9e. 2.5 percent of the population scored below what value? _______ 10. On which test did the student do relatively better on : Test One: A grade of 43 on a test with x 40 and s = 3. Test Two: A grade of 75 on a test with x 72 and s = 5. ___________________ 11. Find the coefficient of variation for each set of scores. Which set has more variation? Cvar ____ Data Set 1: mean 42.5 lbs standard dev 3.7 lbs Cvar ____ Data Set 2: mean 103 lbs standard dev Data set: 16 16 8 48 56 8 40 64 64 72 88 24 18.6 lbs 8 64 _____________________ 12. Find the percentile rank for data point 72 The test scores of 40 students are listed below. 30 35 43 59 62 63 72 73 74 81 82 83 Find the following _______ 13. P65 44 65 76 85 47 66 77 89 48 68 77 92 54 69 78 93 ______ 14. Q1 _______ 16. Q3 55 69 79 94 56 71 80 97 57 72 81 98 ______ 15. Median ______17. Percentile Rank for Data Point 85 18. Construct a Box Plot using the given data. Give the five number summary and label them on the boxplot. 82 88 72 91 53 95 86 77 87 a. Five number summary: ____________________________________________ b. 19. Use your TI – 83 calculator to construct boxplots for Gross ($) in millions for Rrated and PG-13 rated movies. R – rated PG – 13 Title Aliens Braveheart Chasing Amy Executive Decision Good Will Hunting Halloween Hard Rain I Know What You Did Last Summer Pulp Fiction Saving Private Ryan Schindler’s List Scream Terminator The Game True Lies Gross (in millions) 81.843 75.6 12.006 68.75 138.339 47 19.819 72.219 8 178.091 96.067 103.001 36.9 48.265 146.261 Title Armageddon As Good As It Gets Dante’s Peak Deep Impact Forrest Gump Ghost Independence Day Indiana Jones Men In Black Multiplicity Speed 2 The American President The Fifth Element The Man in the Iron Mask Titanic Volcano Gross(in millions 194.125 147.54 67.155 140.424 329.691 217.631 306.124 197.171 250.147 20.1 48.068 65 63.54 56.876 600.743 47.474 a) Give the 5 number summary for both: R-rated: ______________________________________________ PG-13 rated:____________________________________________ b) Change your type of graph to a modified box plot and list any outliers for both list( if none exists, write none) R-rated: _________ PG -13 rated ________ ___________ c) Based on these results, do R-rated or PG-13 movies generally make more money. ______ 20. What is the probability of an event that is certain to occur? A. .5 B. 1 C. .95 D. .99 _______ 21. A die with 6 sides is rolled. What is the probability of rolling a number less than 5? A. 5/6 B. 2/3 C. 4 D. 1/6 ________ 22. The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Men Women Total 382 403 785 Occasional Smoker 37 31 68 Regular Smoker 60 74 134 Heavy Smoker 34 37 71 Total 513 545 1058 If one of the 1058 people is randomly selected, find the probability that the person is a man or a heavy smoker. A. .488 B. .552 C. .479 D. .520 23. ONE card is drawn from a standard card deck. following. You may leave your answers unreduced. Determine each of the _________ 23a. P(Ace of hearts) _________ 23b. P(Ace or King) _________ 23c. P(Ace of spades|the card is black) 24.Two cards are to be drawn from a standard card deck with replacement. Determine each of the following. You may leave your answers unreduced. _________ 24a. Probability that the first card is an ace and the second is a king. _________ 24b. Probability that the first card is an ace and the second card is not and ace. 25. Two cards are to be drawn from a standard card deck without replacement. Determine each of the following. You may leave your answers unreduced. _________ 25a. Probability that the first card is an ace and the second is a king. _________ 25b. Probability that the first card is an ace and the second card is not and ace. _________ 26. A group of five students will be selected from a class of 20 to participate in a survey. In how many ways can the group be selected? _________ 27. A men’s clothing store is offering mix and match sport jackets and slacks. There are 8 different jackets and 12 different slacks. If a man buys one of each how many different outfits could he purchase? _________ 28. In how many ways can 7 books be arranged on a shelf? _________ 29. Ten girls try out for a swim team. How many teams of 6 girls can be chosen? _________30.How many ways can you rearrange the letters of the word “winning”? _________31. If the digits 0-9 are placed in a hat, what is the probability of randomly selecting an odd digit or a digit less than 3? _________32. The odds in favor of winning the door prize are 2:15. What is the probability of winning the prize? 1 _________33. The probability of Becky winning the tennis tournament is . What 8 are the odds against her winning the tournament? __________ 34. Six college buddies bought each other Christmas gifts. They spent: $236.88 $299.92 $150.51 $154.55 $290.97 $251.46 What was the mean amount spent? Round your answer to the nearest cent. ________ 35. Find the mode : 79,25,79,13,25,29,56,79 ________ 36. The weights(in ounces) of 18 cookies are shown. Find the midrange. .68 1.29 1.33 23 26 33 22 13 1.29 1.20 1.46 .93 .68 .74 1.02 1.46 1.33 .74 1.33 1.02 1.43 1.14 .93 __________ 37. The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. Find the median number of vehicles going through the line in a 15-minute period. 25 23 26 23 28 25 29 29 27 29 23 18 25 25 25 ___________ 38. A company had 80 employees whose salaries are summarized below. Find the mean salary from the frequency distribution table. Salary ($) Employees 5,001-10,000 18 10,001- 15,000 20 15,001-20,000 20 20,001-25,000 14 25,001-30,000 8