Question

In New York State, the mean salary for high school teachers in 2017 was $99,410 with a standard deviation of $9,580. Only Alaska's mean salary was higher! Assume New York's state salaries follow a normal distribution

a. What percent of New York's state high school teachers earn between $85,000 and $90,000?
b. What percent of New York's state high school teachers earn between $90,000 and $105,000?

Answer 1

To find the percent of New York's state high school teachers who earn between $85,000 and $90,000, we need to calculate the z-scores for both salary values and use the standard normal distribution table.

Step-by-step explanation:

To find the percent of New York's state high school teachers who earn between $85,000 and $90,000, we need to calculate the z-scores for both salary values and use the standard normal distribution table.

We use the formula z = (x - mean) / standard deviation to calculate the z-scores.

For $85,000: z = (85000 - 99410) / 9580 = -1.4559

For $90,000: z = (90000 - 99410) / 9580 = -0.9468

Looking up the corresponding probabilities in the standard normal distribution table:

The probability of earning less than $85,000 would be the area to the left of z = -1.4559, which is 0.0726 (or 7.26% rounded to the nearest hundredth).

The probability of earning less than $90,000 would be the area to the left of z = -0.9468, which is 0.1711 (or 17.11% rounded to the nearest hundredth).

Therefore, the percent of New York's state high school teachers who earn between $85,000 and $90,000 is approximately 17.11% - 7.26% = 9.85% (rounded to the nearest hundredth).