Analysis of Annual Dental Insurance Costs for XYZ Employees

Analysis of Annual Dental Insurance Costs for XYZ Employees

To find the portion of employees at XYZ Company who cost more than $1,500 per year for dental expenses, we need to calculate the z-score and then find the corresponding percentage using the standard normal distribution table. The information for XYZ Company’s dental expenses is as follows:

Mean (μ) = $1,280

Standard Deviation (σ) = $420

Z-score formula:

z = (X – μ) / σ, where X is the value we want to find the percentage for, μ is the mean, and σ is the Standard Deviation.

Let X = $1,500

z = (1,500 – 1,280) / 420 ≈ 0.524

Now, we need to find the percentage of data that falls to the right of z = 0.524 in the standard normal distribution table. The percentage represents the portion of employees who cost more than $1,500 per year for dental expenses. Looking up the z-table, we find that the percentage corresponding to z = 0.524 is approximately 70%. Therefore, approximately 70% of employees at XYZ Company cost more than $1,500 per year for dental expenses.

Suppose the national study of dental expenses follows a normal distribution with a mean cost of $1,200 and a standard deviation of $400 per year. Now, we want to determine how the dental expenses at XYZ Company compare to the national average. For XYZ Company’s dental expenses:

Mean (μ) = $1,280

Standard Deviation (σ) = $420

For the national study:

Mean (national μ) = $1,200

Standard Deviation (national σ) = $400

First, let’s calculate the z-score for the cost of dental expenses at XYZ Company with respect to the national average:

z = (XYZ Company’s Mean – National Mean) / National Standard Deviation

z = ($1,280 – $1,200) / $400 = $80 / $400 = 0.2

The z-score of 0.2 tells us how many standard deviations XYZ Company’s mean dental expense is above the national mean. Since the z-score is positive, it indicates that XYZ Company’s dental expenses are higher than the national average. The calculated z-score of 0.2 suggests that XYZ Company’s dental expenses are moderately higher than the national average.

Regarding the independence or dependence of the two samples, XYZ Company and the national study, since the national study involved a completely separate and independent group of individuals from XYZ Company’s study, then the samples are considered independent.

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Click the ‘scenario’ button below to review the topic and then answer the following question:

XYZ offers dental insurance to its employees. A recent study of the plan shows the annual cost per employee followed the normal distribution with a mean of $1280 and a standard deviation of $420 per year. For your answers round to two significant digits.

What portion of the employees cost more than $1,500 per year for dental expenses? Give the answer in percentage rounded to the whole number. What is the z-score? For a comparison, you decide to look at the national study of the dental plan with a mean and a standard deviation. Would the two samples (XYZ and national) be considered independent or dependent? Explain.

The recent pandemic greatly affected the working environment. According to a survey, post-pandemic employees are more than ever demanding changes to policies and benefits in the workplace.

Your organization, XYZ Company, notes several hurdles to attracting and retaining staff in the post-pandemic climate. One example is the employer’s inability to adjust to the remote work arrangement, and another is a lack of pay equity commitment.

In keeping with XYZ Company’s goal to treat employees well, management is looking for feedback to measure the company’s performance as the employer of choice.

You work as the Manager of Workforce Analytics within the Human Resources department. The company is growing rapidly, and your boss, Jane, who is the Chief People Officer (CPO), wants to make sure that the company is treating its employees equitably. She is analysis-driven, so she taps you to work on several projects to uncover any potential issues. Her objectives are to: