Applied statistics

0.4071. If the area is not in the​table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores.

z=

5.2) Use the standard normal table to find the​ z-score that corresponds to the cumulative area

0.1991. If the area is not in the​table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores.

z=

5.3) Use a table of cumulative areas under the normal curve to find the​ z-score that corresponds to the given cumulative area. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the​ z-score 0.049

The cumulative area corresponds to the​ z-score of

5.4) Use the standard normal table to find the​ z-score that corresponds to the given percentile. If the area is not in the​ table, use the entry closest to the area. If the area is halfway between two​ entries, use the​ z-score halfway between the corresponding​ z-scores. If​ convenient, use technology to find the z-score P 2

The​ z-score that corresponds to P2 is

5.5) The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of n=6666​, find the probability of a sample mean being less than 23.2 if =23 and

=1.17

5.6) The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of n=75​, find the probability of a sample mean being greater than

216 if μ=215 and σ=3.8.

For a sample of n=75,the probability of a sample mean being greater than 216 if μ=215 and σ=3.8 is

5.7) The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.9 inches. Assume

σ=2.6 inches. Are you more likely to randomly select 1 woman with a height less than 66.8 inches or are you more likely to select a sample of 22 women with a mean height less than 66.8 inches? Explain.

5.8) The heights of fully grown trees of a specific species are normally​ distributed, with a mean of 77.0 feet and a standard deviation of 5.25 feet. Random samples of size 19 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution.

5.9) Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is $247 with a standard deviation of $67. Random samples of size 29 are drawn from this population and the mean of each sample is determined.

The mean of the distribution of sample means is

5.10) Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally​ distributed, with a mean of 102

pounds and a standard deviation of 38.7 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined.

5.11) The amounts of time employees at a large corporation work each day are normally​ distributed, with a mean of 7.7 hours and a standard deviation of 0.36 hour. Random samples of size 22 and 36 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample​increases? If the sample size is =22​, find the mean and standard deviation of the distribution of sample means. The mean of the distribution of sample means is

5.12) The mean height of women in a country​ (ages 20−​29) is 64.1 inches. A random sample of 75

women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ=2.93.