A population consists of the following five values: 1, 1, 3, 5, 6
tutor4helpyou1. A population consists of the following five values: 1, 1, 3, 5, 6. |
(a) | List all samples of size 3, and compute the mean of each sample. (Round sample means to 2 decimal places.) |
Sample | Values | Sum | Mean |
1 | 1,1,3 | 5 | 1.67 |
2 | 1,1,5 | 7 | 2.33 |
3 | 1,1,6 | 8 | 2.67 |
4 | 1,3,5 | 9 | 3.00 |
5 | 1,3,6 | 10 | 3.33 |
6 | 1,5,6 | 12 | 4.00 |
7 | 1,3,5 | 9 | 3.00 |
8 | 1,3,6 | 10 | 3.33 |
9 | 1,5,6 | 12 | 4.00 |
10 | 3,5,6 | 14 | 4.67 |
(c) | Compute the mean of the distribution of sample means and the population mean.(Round your answers to 1 decimal place.) |
2. A normal population has a mean of 68 and a standard deviation of 6. You select a sample of 52. |
Compute the probability the sample mean is (Round z values to 2 decimal places andfinal answers to 4 decimal places): |
(a) | Less than 67. |
(b) | Between 67 and 69. |
(c) | Between 69 and 70. |
(d) | Greater than 70. |
3.
CRA CDs Inc. wants the mean lengths of the "cuts" on a CD to be 128 seconds (2 minutes and 8 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 6 seconds. Suppose we select a sample of 21 cuts from various CDs sold by CRA CDs Inc. |
(a) | What can we say about the shape of the distribution of the sample mean? |
(b) | What is the standard error of the mean? (Round your answer to 2 decimal places.) |
(c) | What percent of the sample means will be greater than 130 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) |
(e) | What percent of the sample means will be greater than 123 but less than 130 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) |
4. Human Resource Consulting (HRC) is surveying a sample of 68 firms in order to study health care costs for a client. One of the items being tracked is the annual deductible that employees must pay. The state Bureau of Labor reports the mean of this distribution is $499 with a standard deviation of $80. |
(a) | Compute the standard error of the sample mean for HRC. (Round your answer to 2 decimal places.) |
(b) | What is the chance HRC finds a sample mean between $477 and $527? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
(c) | Calculate the likelihood that the sample mean is between $492 and $512. (Round z value to 2 decimal places and final answer to 4 decimal places.) |
(d) | What is the probability the sample mean is greater than $550? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
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