10. The average time to complete a 10K race for a female runner is 64.61 minutes with a standard deviation of 5.18 minutes. Nadine completes her first 10K race in 56.82 minutes. What is Nadine's z-score? Show your work. (Round your answer to 2 decimal places.) 11. The lifetime in miles for a certain brand of tire is normally distributed with a mean of 25,462 miles and a standard deviation of 2,155 miles The tire manufacturer wants to offer a money-back guarantee so that no more than 2% of tires will qualify for a refund. What is the maximum number of miles the manufacturer should guarantee that the tires will last? Include a shaded graph that represents the situation.2. According the the Pew Research Center, the probability of a randomly selected person living in the United States identifying with a particular religious affiliation is shown in the following chart. Protestant Catholic Other Non- Unaffiliated Affiliation Christian Christian Christian Christian "none" Probability 0.466 0.208 0.033 1.06 0.233 What is the probability that a randomly selected person living in the United States would identify as either Protestant or Catholic? Show your work. 3. The random variable X, representing the number of items sold in a week, has the following probability distribution: X 5 P(X = X) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 What is the probability that in a given week there will be at most 2 items sold? Show your work. 4. The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: 5 P(X = x) 0.20 0.30 0.20 0.15 0.10 0.05 What is the probability that there will be at least 3 accidents? Show your work.5. The probability distribution for the number of defects during an 8-hour shift on the assembly line at Wanda's Wooden Widgets is as shown in the chart below. 3 5 P(X = x) 0.50 0.25 0.15 0.06 3.03 0.01 They know for sure that there will be at least 4 defects for the day. What is the probability that the day will end with a total of exactly 4 defects? Show your work. 6. Suppose the scores on an exam are normally distributed with a mean p=71 points, and standard deviation 0=4 points. The instructor wanted to "pass" anyone who scored above 69. What proportion of exams will have passing scores? Include a sketch of a shaded graph that represents the situation. 7. Suppose the scores on an exam are normally distributed with a mean =75 points, and standard deviation =8 points. Suppose that the top 2% of the exams will be given an A+. In order to be given an A+, an exam must earn at least what score? Include a shaded graph that represents the situation. S. Suppose that the battery life for a particular cell phone battery is a normal random variable with u = 8 and = 1.2. What is the probability that a randomly chosen battery lasts less than 9 hours? Include a shaded graph that represents the situation. 9. The number of days (X) after mailout that it takes a utility company to receive payment for a customer's bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days. The last 3.5% of bills will be received more than how many days after mailout? Include a shaded graph that represents the situation