Question

A survey reported that the mean starting salary for college graduates after a three-year program was $35 250.Assume that the distribution of starting salaries follows the normal distribution with a standard deviation of $3 190. What percentage of the graduates have starting salaries: (Round z-score computation to 2 decimal places and the final answers to 4 decimal places.) a. Between $31 700 and $37 600?

Answer 1

To find the percentage of graduates with starting salaries between $31,700 and $37,600, we calculate the z-scores for both salary values and find the corresponding areas under the normal distribution curve. The percentage is found by subtracting the area to the left of the lower z-score from the area to the left of the higher z-score.

Step-by-step explanation:

To find the percentage of graduates with starting salaries between $31,700 and $37,600, we need to calculate the z-scores for both salary values and then find the corresponding areas under the normal distribution curve.

First, we calculate the z-score for $31,700 using the formula: z = (x - mean) / standard deviation. For $31,700: z = (31700 - 35250) / 3190 = -1.11.

Next, we calculate the z-score for $37,600: z = (37600 - 35250) / 3190 = 0.74.

Using a standard normal distribution table or a calculator, we find the area to the left of -1.11 is 0.1335 and the area to the left of 0.74 is 0.7704. Therefore, the percentage of graduates with starting salaries between $31,700 and $37,600 is: 0.7704 - 0.1335 = 0.6369 or 63.69%.