The fuel capacity in gallons of 50 randomly selected cars is shown here. Find each of these. a. Mean b. Modal class. C. Standard deviation. Class Frequency 10-12 6 13-15 4 16-18 14 19-21 15 22-24 8 25-27 2 28-30 1 50

The daily sales (in hundreds of dollars) for a store in one month (30 days) are: 15, 22, 18, 25, 19 12, 17, 24, 20, 23 30, 28, 26, 31, 35 21, 19, 27, 18, 20 16, 15, 32, 30, 17 24, 29, 22, 33, 25 a. Construct a grouped frequency distribution with class intervals of width 5 starting from 12. b. Draw a histogram and state whether the data is symmetric, skewed left, or skewed right.

Question: In a group of 100 students, 60 students study Mathematics, 45 students study Physics, and 25 students study both Mathematics and Physics. Find the probability that a randomly selected student studies: (a) Mathematics. (b) Mathematics only. (c) either Mathematics or Physics. (d) neither Mathematics nor Physics.

A model for lifetimes, with a bathtub-shaped hazard rate, is the ex- ponential power distribution with survival function S(x) exp[(Ax)a]}. = exp{1 - (a) If a = 0.5, show that the hazard rate has a bathtub shape and find the time at which the hazard rate changes from decreasing to increasing. (b) If a = 2, show that the hazard rate of x is monotone increasing.

Time 6. Suppose the density function of a survival random variable is f(x) = 4e2 xexp (2-2e2x). Derive the hazard, cumulative hazard, and survival functions. 96

Need help with part b only

19. Does party affiliation differ among the genders? A review of voter registration in a small town yielded the following table of the number of males and females registered for each party Party Affiliation Democrat Republican Male Female Total 300 600 900 500 300 800 Other 200 100 300 Total 1000 1000 2000 a.) Calculate the conditional distributions for party affiliation among each gender. You may present your results in either a table or a graph. b.) Discuss the relationship between gender and party affiliation in two or three sentences.

15. The mean of four people in a room is 30 years. A new person whose age is 55 years enters the room. The mean age of the five people now in the room is (a) 30 (b) 35 (c) 37.5 (d) 40 (e) Cannot be determined

9. A small school has 10 employees, one of whom is the principal and the others are teachers. Suppose he principal makes $100,000 per year and the other employees make between $40,000 and $50,000 per rear. One day, the principal wins an award and is given a $20,000 raise. Which of the following describes ow the school's mean and median salaries would change? (a) The mean and median would both increase by $2,000. (b) The mean would increase by $12,000 and the median would not change. (c) The mean would increase by $2,000 and the median would not change. (d) The median would increase by $2,000 and the mean would not change. (e) The mean would increase by $2,000, but we cannot determine the change in the median without more information.