STA 2023 - Assignment 3 NAME:________________ Concepts Covered: measures of dispersion, and position. Notes Covered: Note 4 and 5 Sections Covered: 3.2, 3.3 1. [4] Both data sets represented below have a mean of 50. One has a standard deviation of 2.4, and the other has a standard deviation of 5. Which is which? Explain your reasoning. 2. [11] Sample annual salaries (in thousands of dollars) for electrical engineers in Boston and Chicago are listed. a) Find the range, variance, and standard deviation of each data set. (Include the calculator output) b) Interpret the results in context of the real life setting. 3. [9] The amount of Jen's monthly phone bill is normally distributed with a mean of $74 and a standard deviation of $8. What percentage of her phone bills are a. Between $50 and $98? b. Between $74 and $90? c. Less than $58? STA 2023 - Assignment 3 NAME:________________ 4. [9] The mean price of new homes from a sample of houses is $155,000 with a standard deviation of $15,000. Using Chebychev's Rule a. What percentage of homes would be within 2 standard deviations from the mean? b. What percentage of homes would be within 2.5 standard deviations from the mean? c. What percentage of homes have a price between $132,500 and $177,500? 5. [12] The following data set represents the heights (in inches) of students in a statistics class 52 54 55 56 56 56 58 59 60 61 61 63 65 67 68 68 70 71 72 a. Use your calculator to find the five number summary. You may write down the second page of the output. b. Create the boxplot for the data set. c. Describe the shape of the distribution. STA 2023 - Assignment 3 NAME:________________ 6. [12] The following data set gives the number of wins for each Major League Baseball team in 2006 61 62 66 67 70 71 75 76 76 76 78 78 78 79 80 80 82 83 85 86 87 88 88 89 90 93 95 96 97 97 Find the following percentiles. a. P70 b. P75 c. P90 d. P95 7. [15] The weights of 19 high school football players have a bell-shaped distribution, with a mean of 186 pounds and a standard deviation of 18 pounds. Use z-scores to determine if the weights of the following randomly selected football players are unusual. d. 213 pounds e. 141 pounds f. 178 pounds g. 249 pounds h. What would be the highest possible weight a player can have so that his weight is not considered unusual? STA 2023 - Assignment 3 NAME:________________ 8. A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution. a. [12] The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-scores that corresponds to each life span. According to the z-scores, would the life spans of any of the tires be considered unusual? b. [12] The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span