**Title: Analyzing Employee Health Care Costs****Introduction:**A college with 2,150 full-time employees is currently analyzing their health care plan. The average out-of-pocket cost for employees is $1,900, with a standard deviation of $250. A random sample of 30 employees has been selected to analyze their out-of-pocket costs.**Problem Statements and Solutions:**a. **Standard Error of the Mean:** - Calculate the standard error of the mean based on the given data. - Formula: SE = σ / √n - **Solution:** (Round to three decimal places)b. **Probability Sample Mean < $1,890:** - Find the probability that the sample mean will be less than $1,890. - **Solution:** (Round to four decimal places)c. **Probability Sample Mean > $1,900:** - Find the probability that the sample mean will be more than $1,900. - **Solution:** (Round to four decimal places)d. **Probability Sample Mean Between $1,865 and $2,005:** - Find the probability that the sample mean will be between $1,865 and $2,005. - **Solution:** (Round to four decimal places)**Conclusion:**This analysis helps in understanding the distribution of out-of-pocket costs among employees and in making informed decisions about health care benefits. Calculating probabilities of different sample mean intervals provides insights into cost fluctuations and potential financial impacts on employees.

a. Define a random variable X, that is the out0of-pocket cost for the employees.

Answered: A college has 260 full-time employees…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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