Question

1. the distribution of employee salary at a large company is skewed to the right, with mean $75,100 and standard deviation $36,554. because the company had a productive year, the ceo will give every employee a $500 christmas bonus. so an employee with a $60,000 salary would receive an adjusted salary of 60,000+500=$60,500.

what shape would the distribution of adjusted salary have? explain your answer.
find the mean of the distribution of adjusted salary. show your work.
find the standard deviation of the distribution of adjusted salary. show your work.

1. scores on the act college entrance exam can be modeled using a normal distribution with mean missing standard deviation 5. wayne’s score on the act was 27.

what was wayne’s standardized score (z - score) on the act? show all of your work.

any professional schools require applicants to take a standardized test. suppose that such a test. several weeks after the test, pete receives his score report: he got a 63, 73rd percentile. what does this mean?

a list of exam scores for mr. williams’s calculus class:
61 65 72 75 75 78 81 81 85 89 91 98

Explanation:

Question 1

Step1: Shape analysis

Adding a constant to every data point preserves the skewness of the original distribution, so the adjusted salary distribution remains skewed right.

Step2: Calculate new mean

Original mean $\mu = 75100$. Add $\$500$ bonus: $\mu_{\text{adjusted}} = 75100 + 500$

Step3: Calculate new standard deviation

Adding a constant does not change spread: $\sigma_{\text{adjusted}} = 36554$

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Question 2

Step1: Apply z-score formula

Use $z = \frac{x-\mu}{\sigma}$, where $x=27$, $\mu=18$, $\sigma=5$.
$z = \frac{27-18}{5}$

Step2: Compute final z-score

$\frac{9}{5}=1.8$

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Percentile Question

A 73rd percentile score means that Pete scored higher than or equal to 73% of all test takers, and only 27% of test takers scored higher than him on this standardized exam.

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Answer:

1. Adjusted salary distribution shape: Skewed right.

Adjusted mean: $\$75600$
Adjusted standard deviation: $\$36554$

1. Wayne's z-score: $1.8$
2. 73rd percentile meaning: Pete scored better than 73% of test takers.