The incomes in a certain large population of college teachers have a normal distribution with mean $75,000 and standard deviation $10,000. Sixteen (16) teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is more than $77,500?

A. 0.0228
B. 0.1587
C. 0.8413
D. Essentially 0

Option B) 0.1587

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $75,000

Standard Deviation, σ = $10,000

We are given that the distribution of salary of college teachers is a bell shaped distribution that is a normal distribution.

Formula:

Standard error due to sampling:

P(average salary is more than $77,500)

P(x > 77500)

Calculation the value from standard normal z table, we have,  

Option B) 0.1587

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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