Suppose that Jason recently landed job offers at two companies. Company A reports an average salary of $51,500 with a standard deviation of $2,175. Company B reports an average salary of $46,820 with a standard deviation of $5,920. Assume that salaries at each company are normally distributed. Jason's goal is to secure a position that pays $55,000 per year. What are the z ‑scores for Jason's desired salary at Company A and Company B? Please round your answers to two decimal places.

The z-score for Jack's desired salary at company A is 1.61.

The z-score for Jack's desired salary at company B is 1.38.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Company A:

Company A reports an average salary of $51,500 with a standard deviation of $2,175. This means that

Jason's goal is to secure a position that pays $55,000 per year. What isthe z ‑score for Jason's desired salary at Company A?

This is Z when X = 55000. So

The z-score for Jack's desired salary at company A is 1.61.

Company B:

Company B reports an average salary of $46,820 with a standard deviation of $5,920. This means that .

Jason's goal is to secure a position that pays $55,000 per year. What isthe z ‑score for Jason's desired salary at Company B?

This is Z when X = 55000. So

The z-score for Jack's desired salary at company B is 1.38.