To answer these questions, we need to convert the salary amounts to z-scores, which measure how many standard deviations an element is from the mean. The formula for calculating a z-score is:

Z = (X - μ) / σ

where:
- X is the value of the element
- μ is the mean
- σ is the standard deviation

a) Between $35,000 and $40,000?

First, calculate the z-scores for $35,000 and $40,000.

Z(35000) = (35000 - 36280) / 3300 = -0.39
Z(40000) = (40000 - 36280) / 3300 = 1.13

Next, look up these z-scores in a standard normal distribution table or use a calculator that can calculate the area under the standard normal curve. The values are approximately 0.6520 and 0.8708 respectively.

The percentage of graduates with salaries between $35,000 and $40,000 is the area between these two z-scores, which is 0.8708 - 0.6520 = 0.2188, or 21.88%.

b) More than $45,000?

Calculate the z-score for $45,000.

Z(45000) = (45000 - 36280) / 3300 = 2.49

The value from the standard normal distribution table is approximately 0.9936. However, because we want the percentage of graduates with salaries more than $45,000, we need to subtract this value from 1 (the total area under the curve).

So, the percentage of graduates with salaries more than $45,000 is 1 - 0.9936 = 0.0064, or 0.64%.

c) Between $40,000 and $45,000?

We already have the z-scores for $40,000 and $45,000 from parts a) and b).

The percentage of graduates with salaries between $40,000 and $45,000 is the area between these two z-scores, which is 0.9936 - 0.8708 = 0.1228, or 12.28%.

Question

To answer these questions, we need to convert the salary amounts to z-scores, which measure how many standard deviations an element is from the mean. The formula for calculating a z-score is:

Z = (X - μ) / σ

where:
- X is the value of the element
- μ is the mean
- σ is the standard deviation

a) Between $35,000 and $40,000?

First, calculate the z-scores for $35,000 and $40,000.

Z(35000) = (35000 - 36280) / 3300 = -0.39
Z(40000) = (40000 - 36280) / 3300 = 1.13

Next, look up these z-scores in a standard normal distribution table or use a calculator that can calculate the area under the standard normal curve. The values are approximately 0.6520 and 0.8708 respectively.

The percentage of graduates with salaries between $35,000 and $40,000 is the area between these two z-scores, which is 0.8708 - 0.6520 = 0.2188, or 21.88%.

b) More than $45,000?

Calculate the z-score for $45,000.

Z(45000) = (45000 - 36280) / 3300 = 2.49

The value from the standard normal distribution table is approximately 0.9936. However, because we want the percentage of graduates with salaries more than $45,000, we need to subtract this value from 1 (the total area under the curve).

So, the percentage of graduates with salaries more than $45,000 is 1 - 0.9936 = 0.0064, or 0.64%.

c) Between $40,000 and $45,000?

We already have the z-scores for $40,000 and $45,000 from parts a) and b).

The percentage of graduates with salaries between $40,000 and $45,000 is the area between these two z-scores, which is 0.9936 - 0.8708 = 0.1228, or 12.28%.

Knowee AI · Accepted Answer