Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Distribution Review Problems ANSWERS 1. The heights of young American women, X, follows the normal distribution with mean =65.5 inches and standard deviation =2.5 inches. a. What is the chance that a randomly selected female is at least 67 inches tall? b. P(X<62) c. P(X65.5) 2. Among applicants to one law school in 1976 the average LSAT score was 600 with a standard deviation of 100. The LSAT scores followed a normal distribution. a. What is the chance a selected applicant scored above a 750? b. If an applicant’s score was in the 90th percentile, what was her score? c. Do we know what the median score was? What is the difference between mean and median? 3. A flashlight battery is guaranteed to last for 40 hours. Tests indicate that the length of life of these batteries is normally distributed with mean 50 and variance 64. a. What is the chance a battery will fail the guarantee? b. What is the chance a battery will not fail the guarantee? 4. Suppose the population mean subscription price for daily newspapers in the US is $6.50/week (all 7 days); the population standard deviation is $2.00. (Assume the prices are for local subscriptions and the distribution of prices is normal). a. Identify what the population is in this problem. b. If a newspaper is randomly selected from the population, what is the probability its local subscription rate will be at least $8.00/week? c. What is the chance a randomly selected newspaper will have a local subscription rate of less than $4.25 per week? 5. Suppose the population mean family income of Cal State LA students this quarter is $45,500. The population standard deviation is $2738.61. a. Identify what the population is in this problem. b. Calculate the probability that a randomly selected individual from the population has a family income within $500 of the population mean (assume the population of family incomes follows a normal distribution). c. If a random sample of 30 students were taken from the population, calculate the probability that the sample mean income will be within $500 of the actual population mean. d. Suppose instead a sample of 60 students were taken. What is the probability the sample mean will be within $500 of the actual population mean? e. Explain why taking a larger sample is better than taking a smaller one. f. Explain why the normality assumption for the population may not be appropriate for this problem. Distribution Review Problems 1. The heights of young American women, X, follows the normal distribution with mean =65.5 inches and standard deviation =2.5 inches. a. What is the chance that a randomly selected female is at least 67 inches tall? .2743 b. P(X<62) .0808 c. P(X65.5) .5 2. Among applicants to one law school in 1976 the average LSAT score was 600 with a standard deviation of 100. The LSAT scores followed a normal distribution. a. What is the chance a selected applicant scored above a 750? .0668 b. If an applicant’s score was in the 90th percentile, what was her score? 728 c. Do we know what the median score was? What is the difference between mean and median? The median is the middle observation in a data set ordered from lowest to highest. For a symmetric distribution the mean would equal the median. 3. A flashlight battery is guaranteed to last for 40 hours. Tests indicate that the length of life of these batteries is normally distributed with mean 50 and variance 64. a. What is the chance a battery will fail the guarantee? .1056 b. What is the chance a battery will not fail the guarantee? .8944 4. Suppose the population mean subscription price for daily newspapers in the US is $6.50/week (all 7 days); the population standard deviation is $2.00. (Assume the prices are for local subscriptions and the distribution of prices is normal). a. Identify what the population is in this problem. US daily newspapers b. If a newspaper is randomly selected from the population, what is the probability its local subscription rate will be at least $8.00/week? .2266 c. What is the chance a randomly selected newspaper will have a local subscription rate of less than $4.25 per week? .1292 5. Suppose the population mean family income of Cal State LA students this quarter is $45,500. The population standard deviation is $2738.61. a. Identify what the population is in this problem. Cal State LA students this quarter b. Calculate the probability that a randomly selected individual from the population has a family income within $500 of the population mean (assume the population of family incomes follows the normal distribution). .1428 c. If a random sample of 30 students were taken from the population, calculate the probability that the sample mean income will be within $500 of the actual population mean. .6826 d. Suppose instead a sample of 60 students were taken. What is the probability the sample mean will be within $500 of the actual population mean? .84 e. Explain why taking a larger sample is better than taking a smaller one. A larger sample decreases the standard deviation of the sample mean. f. Explain why the normality assumption for the population may not be appropriate for this problem. Large incomes in the population normally skew the distribution to the right. The normal distribution is symmetric. If the sample size is at least 30 observations, the distribution of x is approximately normal, regardless of the distribution of the population.