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Business Math Exam Chapter 10 Name____________________________________ Group Period ___________________ 10.1 -2 Use the following data for all the following questions in 10.1: 74 133 4 127 20 30 103 27 139 118 138 121 149 132 64 141 130 76 42 50 95 56 65 104 4 140 12 88 119 64 a) Make a Frequency Distribution Table using 6 intervals INTERVAL TALLY 0 - 24 b) Find the grouped mean, FREQUENCY MIDPOINT 25 - 49 50 - 74 75 - 99 c) Find the modal class. 100 - 124 125 – 149 Construct a HISTOGRAM and a FREQUENCY POLYGON y x Is the Histogram Left Skewed, Right Skewed, Nornal, or Uniform? __________________________ x 10.3 2) A company often uses “Preformance Ratings” to give promotions and raises and also to fire employees. A Grocery Store checks the time spent in a check-out line ( in minutes) for 13 randomly selected customers during the store’s busiest time: One person was chosen in each of 13 checkout lines serviced by different employees. The minutes the customer waited in the line was measured. 4.6 8.5 6.1 7.8 10.9 9.3 11.4 5.8 9.7 8.8 6.7 13.2 10.9 a) Find the Range: ______________________ b) Find the Median: c) Is there a Mode? ___________ If, YES, what is it? _____________________ d) Find the mean: e) Find the standard deviation (squared) (sample) s = f) Which time(s) lie outside 1 standard deviation of the mean. ___________________ x Below ___________________ Above _________________________ 3) Find the Mean and the Standard Deviation for the scores obtained on recent Calculus Test. SCORE FREQUENCY 90 - 99 6 80 - 89 9 70 - 79 30 60 - 69 15 50 - 59 3 Mean, x , Standard Deviation , s =, 10.4 4) Find the z – score for the following situations. a) Grade of 74 on a test with mean 82 and standard deviation 6.5 5) Find the percent of the area under a normal curve between the indicated numbers. Sketch and shade your answer. A time of 10.8 seconds in a race with μ = 10.1 sec. and σ = .51 y y x a) between the mean and z = 1.4 6) b) x b) between z = -.64 and z = 1.75 A certain brand of 100 – watt light bulb has a mean life of 750 hours and a standard devieation of 50 hours. Assuming that the lives of these bulbs are normally distributed, what proportion of the bulbs will burn a) at least 820 hours b) between 600 and 775 hours 10.5 7) Experinental data indicates that the cure rate of a new drug is 85% . If the drug is given to 100 patients, find the probability that at least 90 of them will be cured. Use The Normal Distribution as an approximation for the Binomial . 8) Actuarial tables indicate an accidental death rate in the United States of 56 persons per 100,000. If an insurance company covers 500,000 individuals for accidental death benefits, what is the probability that the number of claims in a year will be between 260 and 300 (inclusive)? Use The Normal Distribution as an approximation and define success as “filing a claim.” 9) Use the following data for all the following questions 74 133 4 127 20 30 103 27 139 118 138 121 149 132 64 141 130 76 42 50 95 56 65 104 4 140 12 88 119 64 Find the Median and create a BOX PLOT for the data.