Intro to Stats and Analytics

Question

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 65 and a standard deviation of 9. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 38 and 65?

Use 68-95-99.7 and do not enter the percent symbol.

ans = Incorrect %

Answer 1

Hi Lucy,

According to Empirical Rule, 99.7% of observations lie within three standard deviations sigma of the mean mu. Here:

mu = 65

sigma = 9

65 is the mean and we are interested in the number of requests between 38 and 65. 38 is three standard deviations below 65:

65 - 3(9) = 38

Now, we know that 99.7% of data fall within three standard deviations either way, but we want only the low side here, so we divide this by 2. Again, this will be clearer if you draw the distribution

99.7/2 = 49.85% Don't enter the symbol.

I hope this helps. Let me know if you want to schedule a tutoring session to discuss more of these problems.