Question

The average teacher's salary in North Dakota is $35,441. Assume a normal distribution with =σ$5100. Round the final answers to at least 4 decimal places and round intermediate z-value calculations to 2 decimal places.What is the probability that a randomly selected teacher's salary is greater than $47,500?=P>X47,500

Answer 1

The probability that a randomly selected teacher's salary is greater than $47,500 is approximately 0.0083 or 0.83%.

Step-by-step explanation:

To find the probability that a randomly selected teacher's salary is greater than $47,500, we need to calculate the z-score and then find the corresponding area under the normal distribution curve.

The formula for calculating the z-score is:

z = (X - μ) / σ

Where X is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (47500 - 35441) / 5100

= 2.366

Using a z-table or calculator, we can find that the area to the right of 2.366 is approximately 0.0083.

Therefore, the probability that a randomly selected teacher's salary is greater than $47,500 is approximately 0.0083 or 0.83%.