Math 106, Quiz #6. Due 10/8/17: Name: Keenen Edmondson Please show all work. Each problem is worth 10 points. 1. The following table is the final distribution of grades in the introductory economics course at a local university: Grades Number of Students 50 - 59 7 60 - 69 4 70 - 79 10 80 - 89 14 90 - 99 5 a. How many classes are there in the class? 40 b. What percentage of the students scored at least 70 in the test? 72.5% c. Draw a histogram of the scores. students 16 14 12 10 8 6 4 2 0 50-59 60-69 70-79 students d. Estimate the mean score. 80-89 90-99 2. The following data represent a sample of the ages of individuals working at a telephone crisis center. 33, 40, 35, 24, 31, 32, 45, 23, 45, 34, 34, 54, 25, 36, 38, 44, 62, 31, 56, 47, 30, 42, 43, 52, 48, 56, 64, 40, 61, 39, 29, 34, 37, 43, 47, 32, 45, 27, 35, 29 a. Construct a box and whisker plot. What can you say about the data based on this plot? b. Does this data satisfy the empirical rule (68%-95%-99.7% rule)? 3. The mean age of a class of 25 students is 23.4 years. How old will a 26 th student have to be in order for the mean age of the class to be 24 years? 4. The average annual salary of 15 employees at a certain manufacturing plant is $36,500 and the median salary is $32,250. If the highest paid employee received a raise of $3,560, a. what is the new average salary for the 15 employees? b. what is the new median salary for the 15 employees? 5. A box contains eight golf balls. Four of these balls are not perfectly round. If three balls are randomly selected without replacement, what is the probability that at least one is not perfectly round? 6. If the mean salary of 18 men in a certain manufacturing plant is $45,000 and the mean salary of 12 women in the same plant is $38,000, what is the mean salary of all the 30 employees? 7. The auto parts department of an automotive dealership sends out an average of eight special orders daily. The number of special orders is assumed to follow a Poisson distribution. a. What is the probability that for any day, the number of special orders sent out will be more than four? b. What is the standard deviation of the number of special orders sent out daily? 8. If P(A) = .70; P(B) = .30, and P(A and B) = .20, find the following probabilities. a. b. P( A or B) P( A | B ) 9. Todd Booth, an avid jogger, kept detailed records of the number of miles he ran per week during the past year. The frequency distribution in the figure below summarizes his records. Find the mean, median, and mode of the number of miles per week that Todd ran. Miles Run per Week 0 1 2 3 4 5 6 7 Number of Weeks 4 5 10 9 10 7 4 3 a. Mean number of miles = b. Median number of miles = c. Mode number of miles = 10. Christian D'Angelo has scores of 68, 65, 75, and 78 on his statistics tests. Find the scores he can make on his final exam to receive a C in the course. The final exam counts as two test scores and C is received if the final course grade is from 70 to 79