# National Highway Traffic Safety Administration

Probability 6.75:The U.S. National Highway Traffic Safety Administration gathers data concerning the causes of highway crashes where at least one fatality has occurred. The following probabilities were determined from the 1998 annual study (BAC is blood-alcohol content).Source: Statistical Abstract of the United States, 2000, Table 1042.P(BAC= 0 0 Crash with fatality) = .616P(BACis between .01 and .09 0 Crash with fatality) = .300P(BACis greater than .09 0 Crash with fatality) = .084 Over a certain stretch of highway during a 1-year period, suppose the probability of being involved in a crash that results in at least one fatality is .01. It has been estimated that 12% of the drivers on this highway drive while their BAC is greater than .09. Determine the probability of a crash with at least one fatality if a driver drives while legally intoxicated (BAC greater than .09). In order to solve the problem use Bayes Theorem

Probability 6.81: Your favorite team is in the final playoffs. You have assigned a probability of 60% that it will win the championship. that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over; your team has lost. What is the probability that it will win the series? In order to solve the problem use the Bayes Theorem for this equation also.

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Estimation 10.14 A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that x is 10. Estimate the population mean with 90% confidence.

Hypothesis Testing 11.52: The operations manager of a would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 6 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds? Assume that the confidence level is to be 99%.

Inference about Population 12.85: a. A to test the following hypotheses:

H0:p= .70

H1:p> .70

A random sample of 100 produced ^p = .73. Calculate the p-value of the test.

b. Repeat part (a) with ^p = .72.

c. Repeat part (a) with = ^p .71.

d. Describe the effect on the z-statistic and its p-value of decreasing the sample proportion.

Inference about Population 12.76: Some that the major cause of highway collisions is the differing speeds of cars. That is, when some cars are driven slowly while others are driven at speeds well in excess of the speed limit, cars tend to congregate in bunches, increasing the probability of accidents. Thus, the greater the variation in speeds, the greater will be the number of collisions that occur. Suppose that one expert believes that when the variance exceeds 18 mph2, the number of accidents will be unacceptably high. A random sample of the speeds of 245 cars on a highway with one of the in the country is taken. Can we conclude at the 10% significance level that the variance in speeds exceeds 18 mph2?

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