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Martha, A statistician wishes to analyze teachers’ salaries in the state of California. She determines that teacher’s salaries in California are normally distributed with a mean salary of $37,764 and a standard deviation of $5,100. Answer the following questions. a) What is the probability that a randomly selected teacher’s salary in California is greater than $45,000?

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Answer:

0.078 or 7.8%

Step-by-step explanation:

Mean salary (μ) = $37,764

Standard deviation (σ) = $5,100

The z-score for any given teacher's salary in California, X, is determined by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = $45,000:

[tex]z=\frac{45,000-37,764}{5,100}\\ z=1.419[/tex]

A z-score of 1.419 corresponds to the 92.20th percentile of a normal distribution. Therefore, the probability that a salary is greater than $45,000 is:

[tex]P(X>\$45,000) = 1-0.9220\\P(X>\$45,000) = 0.078=7.8\%[/tex]

The probability is 0.078 or 7.8%.

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