MATH 534 Week 3 Homework Problems (v1)

1. Question: Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the z-value for a score of 80? 2. Question: Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the probability of obtaining a score less than 80? 3. Question: Which one of the following is not a characteristic of a normal distribution? 4. Question: If the z-value of a given x value is positive, it means that ___________. 5. Question: Assume a normal distribution and find the following probabilities. 6. Question: Suppose X is normally distributed with mean 50 and standard deviation 4, what is P(45 < X < 58)? 7. Question: Suppose X is normally distributed with mean 20 and standard deviation 4, find the value x0 such that P(X ≥ x0) = 0.975. 8. Question: According to the Air Transport Association of America, the average operating cost of an MD-80 jet airliner is $2,087 per hour. Suppose the operating costs of an MD-80 jet airliner are normally distributed with a standard deviation of $173 per hour. 9. Question: In a recent year, the average daily circulation of the Wall Street Journal was 2,276,207. Suppose the standard deviation is 70,940. Assume the paper’s daily circulation is normally distributed 10. Question: Selection of the winning numbers is a lottery is an example of ___________. 11. Question: A type of random sampling in which every k th item (where k is some number) in the population is selected for inclusion in the sample is called ___________. 12. Question: Suppose samples of size 100 are drawn randomly from a normal population that has a mean of 20 and a standard deviation of 5. What is the probability of observing a sample mean less than 19? 13. Question: Suppose samples of size 100 are drawn randomly from a normal population that has a mean of 20 and a standard deviation of 5. What is the probability of observing a sample mean between 19 and 20.5? 14. Question: Suppose samples of size 100 are drawn randomly from a normal population that has a mean of 20 and a standard deviation of 5. What are the values of the mean and the standard deviation of the distribution of the sample means? 15. Question: Suppose the age distribution in a city is as follows. 16. Question: A researcher is conducting proportionate stratified random sampling with a sample size of 300. Approximately how many people should he sample from each stratum? 17. Question: The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following?