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The average salary for a Queen College full professor is $85,900. If the average salaries are normally distributed with a standard deviation of $11,000 find these probabilities:a.    The professor makes more than $90,000b.    The professor makes more than $75,000

Question

The average salary for a Queen College full professor is $85,900. If the average salaries are normally distributed with a standard deviation of $11,000 find these probabilities:

a.    The professor makes more than $90,000

b.    The professor makes more than $75,000

check_circleAnswer
Step 1

It is given that mean and standard deviation are $85,900 and $11,000, respectively.

The random variable X represents salary for a Queen College full professor.

Step 2

a)

The probability that the professor makes more than $90,000 is obtained as follows:

x-L
90,000 85,900
Z =
11,000
z 0.37
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x-L 90,000 85,900 Z = 11,000 z 0.37

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Step 3

The probability that the professor makes more than $90,000 represents the area to the right of 0.37.

Here, the area to the left of 0.37 using standard n...

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