Question 1: Make a frequency distribution and histogram (using appropriate bins) for these 28 observations on the amount spent for dinner for four in downtown Chicago on Friday night. (b) Repeat the exercise, using a different number of bins. Which is preferred? Why? Dinner
95 103 109 170 114 113 107
124 105 80 104 84 176 115
69 95 134 108 61 160 128
68 95 61 150 52 87 136
Question 2: On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below. (a) FindP(X ≥ 3). (b) Find P(X ≤ 2). (c) Find P(X <, 4). (d) FindP(X = 1). (e) Which of the probability expressions in parts (a)-(d) is a value of the CDF?
x 0 1 2 3 4 5 Total
P(x) .05 .30 .25 .20 .15 .05 1.00
Question3: Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class.
a) Find the mean, median, and mode for each quiz.
b) Do these measures of center agree? Explain.
c) For each data set, note strengths or weaknesses of each statistic of center.
d) Are the data symmetric or skewed? If skewed, which direction?
e) Briefly describe and compare student performance on each quiz.
Quizzes:
- Quiz 1: 60, 60, 60, 60, 71, 73, 74, 75, 88, 99
- Quiz 2: 65, 65, 65, 65, 70, 74, 79, 79, 79, 79
- Quiz 3: 66, 67, 70, 71, 72, 72, 74, 74, 95, 99
- Quiz 4: 10, 49, 70, 80, 85, 88, 90, 93, 97, 98
Question 4: Let S be the event that a randomly chosen female aged 18-24 is a smoker. Let C be the event that a randomly chosen female aged 18-24 is a Caucasian. Given P(S) = .246, P(C) = .830, and P(S ?C) = .232, find each probability.
a. P(S′).
b. P(S ? C).
c. P(S | C).
d. P(S | C′).
Question 5: Discuss why you would or would not expect each of the following variables to be normally distributed. Hint: Would you expect a single central mode and tapering tails? Would the distribution be roughly symmetric? Would one tail be longer than the other?
a. Shoe sizes of adult males.
b. Years of higher education of 30-year-old employed women.
c. Days from mailing home utility bills to receipt of payment.
d. Time to process insurance claims for residential fire damage.