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 43 and a standard deviation of 8. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 19 and 43?

Answer 1

Hello Sir/ Mam

THE REQUIRED ANSWER IS 49.85%

The 68-95-99.7 rule states that in case the distribution is normal:

• Approxiately 68% of the observations lie within 1 Standard deviation of the mean.
• Approxiately 95% of the observations lie within 2 Standard deviation of the mean.
• Approxiately 99.7% of the observations lie within 3 Standard deviation of the mean.

Hence,

Given that :

Mean = 43

Standard Deviation = 8

Range is 19 to 43

Similarly,

Hence,

As 99.7% of the observations will lie in ,

Hence,

In, , there will be of the observations.

I hope this solves your doubt.

Do give a thumbs up if you find this helpful.