Please provide calculation processes below your answers to receive partial points. Please round the answers (related to probability-related questions) to four decimal places. Four- points for each question.
(1-6) Let's assume that the time to fly between Houston and Las Vegas is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes.
1. What is the distribution's mean?
2. What is the distribution's standard deviation?
3. What is the uniform probability of the distribution?
4. What is the probability that a flight is less than 135 minutes?
5. What is the probability that a flight is more than 140 minutes?
6. What is the probability that a flight is between 125 and 140 minutes?
(7-10) Please use the table for "areas under the normal curve" to answer the following questions.
7. What is the area under the normal curve between z = 0.00 and z = 1.79?
8. For a standard normal distribution, what is the probability that z is greater than 1.75?
9. What is the area under the normal curve between z = -1.0 and z = -2.0?
10. What is the probability that z is between 0.0 and -2.0?
(11-18) The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. Please use the table for "areas under the normal curve" to answer the following questions.
11. Assuming a normal distribution, what is the probability that a student scored between 70 and 84?
12. Assuming a normal distribution, what is the probability that a student scored 90 or higher?
13. Assuming a normal distribution, what is the probability that a student scored greater than 65?
14. Assuming a normal distribution, what is the probability that a student scored between 63 and 77?
15. Assuming a normal distribution, what is the probability that a student scored between 56 and 63?
16. Assuming a normal distribution, what is the probability that a student scored between 77 and 84?
17. Assuming a normal distribution, what test score separates the top 5% of the students from the lower 95% of the students?
18. Assuming a normal distribution, what test score separates the top 25% of the students from the lower 75% of students?
(19-25) Please use the table for "areas under the normal curve" to answer the following questions.
19. The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400, the standard deviation is 50. What is the area under the normal curve between 400 and 482?
20. Customers of the Key Refining Company charge an average of $70 per month. The distribution of amounts charged is approximately normal, with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?
21. Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 4.95% of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?
22. Management is considering a bonus system to increase production. One suggestion is to pay a bonus on the highest 4.95% of production based on past experience. Past records indicate that an average of 4,000 units of a small assembly is produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5% of production, the bonus will be paid on how many units or more?
23. The annual commissions per salesperson employed by a retailer of mobile communication devices averaged $40,000, with a standard deviation of $5,000. What probability of the salespersons earn between $32,000 and $42,000?
24. The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. The probability that a bag of corn chips weighs between 20.75 and 23.25 ounces is ____.
25. The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95% of the observations lie between what two values? (hint: please refer to the empirical rule in p. 8, Chapter 7).