Question

1. Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the following probabilities. (Round all answers to four decimal places.)

(c) P(0.40 < z < 0.85) =
(d) P(−0.85 < z < −0.40) =
(e) P(−0.40 < z < 0.85) =

2. Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that

P(A beats B) = 0.6
P(A beats C) = 0.2
P(B beats C) = 0.4

(d) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)

3.

Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean μ = 6 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the following probabilities. (Round your answers to four decimal places.)

(a) P(x > 6) =

(b) P(x < 6.2)=

(c) P(x ≤ 6.2) =

(d) P(5.6 < x < 6.2) =

(e) P(x > 5.7) =

(f) P(x > 4.8) =

4.

In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5,000 accidents, the average speed was 44 mph and the standard deviation was 14 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.)

(a)

Approximately what percentage of vehicle speeds were between 30 and 58 mph?

approximately  %

(b)

Approximately what percentage of vehicle speeds exceeded 58 mph? (Round your answer to the nearest whole number.)

approximately  %

5. In a survey of 485 potential jurors, one study found that 340 were regular watchers of at least one crime-scene forensics television series.

(a) Assuming that it is reasonable to regard this sample of 485 potential jurors as representative of potential jurors in the United States, use the given information to construct a 95% confidence interval for the true proportion of potential jurors who regularly watch at least one crime-scene investigation series. (Use Table 3 in Appendix A. Give the answer to three decimal places.)

Answer 1