Normal Distribution and Random Sample
Math 156–Sat: HW #4 Name:
1. What is the difference between [pic] and[pic]? Between s and[pic]? (10 points)
2. Explain the difference between [pic] and [pic] and between [pic] and[pic]? (10 points)
3. Suppose that a random sample of size 64 is to be selected from a population having [pic] and standard deviation 5.
(a) What are the mean and standard deviation of the [pic] sampling distribution? Can we say that the shape of the distribution is approximately normal? Why or why not? (10 points)
(b) What is the probability that [pic] will be within 0.5 of the population mean? (5 points)
(c) What is the probability that [pic] will differ from the population mean by more than 0.7? (5 points)
4. In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 pounds. Assume that the average weight of students, faculty, and staff on campus is 150 pounds with a standard deviation of 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is taken:
(a) What is the mean and standard deviation of the [pic] = sample mean distribution? Can we assume the [pic] distribution is normal? Explain. (10 points)
(b) What average weights of for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 pounds? (5 points)
(c) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (5 points)
5. A random sample is to be selected from a population that has a proportion of successes[pic]. Determine the mean and standard deviation of the sampling distribution of p for each of the following sample sizes. (5 points each)
(a) n = 10
(b) n = 20
(c) n = 29
(d) n = 200
6.
1. What is the difference between [pic] and[pic]? Between s and[pic]? (10 points)
2. Explain the difference between [pic] and [pic] and between [pic] and[pic]? (10 points)
3. Suppose that a random sample of size 64 is to be selected from a population having [pic] and standard deviation 5.
(a) What are the mean and standard deviation of the [pic] sampling distribution? Can we say that the shape of the distribution is approximately normal? Why or why not? (10 points)
(b) What is the probability that [pic] will be within 0.5 of the population mean? (5 points)
(c) What is the probability that [pic] will differ from the population mean by more than 0.7? (5 points)
4. In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 pounds. Assume that the average weight of students, faculty, and staff on campus is 150 pounds with a standard deviation of 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is taken:
(a) What is the mean and standard deviation of the [pic] = sample mean distribution? Can we assume the [pic] distribution is normal? Explain. (10 points)
(b) What average weights of for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 pounds? (5 points)
(c) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (5 points)
5. A random sample is to be selected from a population that has a proportion of successes[pic]. Determine the mean and standard deviation of the sampling distribution of p for each of the following sample sizes. (5 points each)
(a) n = 10
(b) n = 20
(c) n = 29
(d) n = 200
6.