Human Resource Consulting (HRC) surveyed a random sample of 60 Twin Cities construction companies to find information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is $502 with a standard deviation of $100.
a. Compute the standard error of the sample mean for HRC.
b. What is the chance HRC finds a sample mean between $477 and $527?
c. Calculate the likelihood that the sample mean is between $492 and $512.
d. What is the probability the sample mean is greater than $550?
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From the given information we have the population mean and standard deviation and the sample size is
Because the sample size is large enough at 60, assume normality of the sampling distribution.
(a)
Compute the standard error.
The standard error of the mean is defined to be:
Plug in 205 for the population standard deviation and 60 in for the sample size to calculate the standard error of the mean:
Thus, the standard error of the sample mean is approximately $12.91.
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