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 61 and a standard deviation of 9. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 34 and 61?

Answer 1

According to 68-95-99.7 rule, 68%, 95% and 99.7% of data values lie within 1, 2 and 3 standard deviations of mean.

Here, mean = 57

Standard deviation = 11

The value 57 is the mean and hence, 50% of values are above mean

57 + 2 x 11 = 79

79 is 2 standard deviations above mean

Of the 95% that lies within 2 standard deviations of mean, half lies above mean and half lies below mean.

Therefore, approximate percentage of lightbulb replacement requests numbering between 57 and 79 = 95/2

= 47.5%

Answer 2

Answer: 49.85%

Explanation:

Given : 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 ( normal distribution ) and has a mean of 61 and a standard deviation of 9.

i.e.
`\mu=61` and
`\sigma=9`

To find : The approximate percentage of lightbulb replacement requests numbering between 34 and 61.

i.e. The approximate percentage of lightbulb replacement requests numbering between 34 and
`34+3(9)`.

i.e. i.e. The approximate percentage of lightbulb replacement requests numbering between
`\mu` and
`\mu+3(\sigma)`. (1)

According to the 68-95-99.7 rule, about 99.7% of the population lies within 3 standard deviations from the mean.

i.e. about 49.85% of the population lies below 3 standard deviations from mean and 49.85% of the population lies above 3 standard deviations from mean.

i.e.,The approximate percentage of lightbulb replacement requests numbering between
`\mu` and
`\mu+3(\sigma)` = 49.85%

⇒ The approximate percentage of lightbulb replacement requests numbering between 34 and 61.= 49.85%