4. (13 pts) The IQ scores of 50 students are given below. 85 86 87 87 90 90 92 93 94 94 94 94 96 96 96 97 97 98 100 100 101 101 102 103 103 103 104 104 105 106 106 106 107 107 107 107 108 110 110 111 111 111 111 114 115 115 115 118 119 119 Construct a grouped frequency distribution for the data. Use 85-89 for the first class and use the same width for each subsequent class. Class Frequency 85-8914. Suppose that the speed at which cars go on the freeway is normally distributed with mean 74 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. a. (2 pts) What is the distribution of X? X ~ N( b. (3 pts) If one car is randomly chosen, find the probability that it is traveling more than 79 mph. Round to 4 decimal places. c. (3 pts) If one of the cars is randomly chosen, find the probability that it is traveling between 70 and 75 mph. Round to 4 decimal places.10.A store manager gathers some demographic information from the store's customers. The following chart summarizes the age-related information they collected: Age Number of Customers of 12 ZOOM + 7. A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 257 members were looked at and their mean number of visits per week was 3.1 and the standard deviation was 2.1. Round answers to 3 decimal places where possible. a. (1 pt) Fill in the blank: To compute the confidence interval use a distribution. b. (6 pts) With 90% confidence the population mean number of visits per week is between and visits. c. (1 pt) If many groups of 257 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week. Suppose that textbook weights are normally distributed. You measure 55 textbooks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 13.2 ounces. a. (1 pt) What is X? b. (1 pt) What is o? c. (6 pts) Based on this, construct a 90% confidence interval for the true population mean textbook weight. Round answers to 2 decimal places.11. (4 pts) Complete the following probability distribution table: Probability Distribution Table X P(X) -29 0.3 47 51 0.2 66 0.2 LE L 12.(8 pts) Here is a set of sample data 10 17 22 24 25 32 34 41 57 73 78 84 93 94 100 Identify the 5 number summary (min, Q1, median, Q3, max) Min = 01 = Median = 03 = Max =9. You are playing a card game, and the probability that you will win a game is p = 0.27. a. (3 pts) If you play the game 150 times, what is the most likely number of wins? (Round answer to one decimal place.) LL = b. (3 pts) Let X represent the number of games (out of 150) that you win. Find the standard deviation for the probability distribution of X. (Round answer to two decimal places.) O= c. (2 pts) The range rule of thumb specifies that the minimum usual value for a random variable is u-20 and the maximum usual value is u+20. You already found u and o for the random variable X. Use the range rule of thumb to find the usual range of X values. Enter answer as an interval using square-brackets and only whole numbers. usual values =T-Mobile Wi-Fi 12:34 AM 16% Take Quiz Exit MAT 123 Final Exam Fall 2022 i X Version A.pdf Page 6 > of 12 ZOOM + 5. (4 pts) Temperatures in June in the Paradise City are distributed nearly normally with mean 85 degrees and standard deviation 5 degrees F. Which of the following temperatures would be considered unusual? Circle your answer. a. 78 b. 84 c. 79.5 G d. 83.5 e. 72.5 S LE 6. (4 pts) 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 . 689 b=32 . 456 r2=0 . 499849 r=-0. 707 Use this to predict the number of situps a person who watches 15 hours of TV can do (to one decimal place).13. The following refer to the following data set: 65 64 45 20 90 26 73 35 65 63 a. (3 pts) What is the mean of this data set? mean = (Please show your answer to one decimal place.) b. (3 pts) What is the median of this data set? median = L c. (2 pts) What is the mode of this data set? mode =