The mean salary for the engineering department of a large company is 100,000. The salaries for the engineering department follow a normal distribution. About 95% of the salaries are between 60,000 and 140,000. What is the standard deviation of the salaries for the engineering department?
This is a statistics problem. The answer is 20,000. I just want to know how to solve it. Thank you so much, please explain.
2007-06-12 13:12:41 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
In a normal distribution, there are three handy rules to remember:
About 68% of the distribution lies within 1 standard deviation of the mean.
About 95% of the distribution lies within 2 standard deviations of the mean.
About 99.7% of the distribution lies within 3 standard deviations of the mean.
The second one is useful in this case. We know the mean salary is 100,000, and that 95% of the salaries are between 60,000 and 140,000. Since 95% of the salary distribution lies within 2 standard deviations of the mean (in EITHER direction), it becomes clear that 60,000 and 140,000 are both 2 standard deviations away from the mean. Each of these endpoints is 40,000 away from the mean, so a distance of 2 standard deviations from the mean is 40,000. Therefore, a distance of 1 standard deviation from the mean is 20,000.
2007-06-12 13:24:14 · answer #1 · answered by lithiumdeuteride 7 · 1⤊ 0⤋
For a normal curve, one standard deviation accounts for about 68% of the population, and 2 standard deviations cover 95%.
In your normal curve, the mean would be midway between the 60K and 140K and the ends are two standard deviations away from the mean.
2007-06-12 13:26:17 · answer #2 · answered by astatine 5 · 0⤊ 0⤋