Question

The annual salaries earned by executes at Fortune 500 companies are normally distributed. The mean salary is $770,000 and the standard deviation is $32,000. What is the cutoff salary for the top 15% of executives (please choose the value closest to your answer)?

811000
822600
797000
803100
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Answer 1

The cutoff salary for the top 15% of executives is $797,280.

Step-by-step explanation:

To find the cutoff salary for the top 15% of executives, we need to find the z-score that corresponds to the top 15% of the standard normal distribution.

1. First, we convert the given salary to a z-score using the formula: z = (x - mean) / standard deviation. For the cutoff salary, x = cutoff salary, mean = $770,000, and standard deviation = $32,000.
2. We then use a z-table or a calculator to find the z-score that corresponds to the top 15% of the standard normal distribution. In this case, the z-score is approximately 1.04.
3. Finally, we can find the cutoff salary by rearranging the z-score formula: cutoff salary = z * standard deviation + mean. Plugging in the values, we have: cutoff salary = 1.04 * $32,000 + $770,000 = $797,280.

Therefore, the cutoff salary for the top 15% of executives is $797,280.

Answer 2

The cutoff salary for the top 15% of executives is $797,280.

Step-by-step explanation:

To find the cutoff salary for the top 15% of executives, we need to find the z-score that corresponds to the top 15% of the standard normal distribution.

1. First, we convert the given salary to a z-score using the formula: z = (x - mean) / standard deviation. For the cutoff salary, x = cutoff salary, mean = $770,000, and standard deviation = $32,000.
2. We then use a z-table or a calculator to find the z-score that corresponds to the top 15% of the standard normal distribution. In this case, the z-score is approximately 1.04.
3. Finally, we can find the cutoff salary by rearranging the z-score formula: cutoff salary = z * standard deviation + mean. Plugging in the values, we have: cutoff salary = 1.04 * $32,000 + $770,000 = $797,280.

Therefore, the cutoff salary for the top 15% of executives is $797,280.