Question

The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 37 and a standard deviation of 10. iS Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 37 and 67?

Answer 1

Answer: 49.85%

Step-by-step explanation:

From the information given,

mean = 37

standard deviation = 10

The 68-95-99.7 rule states that 68% of the data fall within 1 standard deviation of the mean. 95% of the data fall within 2 standard deviations of the mean and 99.7% of the data fall within 3 standard deviations of the mean. Thus,

1 standard deviation to the left of the mean = 37 - 10 = 27

1 standard deviation to the right of the mean = 37 + 10 = 47

3 standard deviation to the left of the mean = 37 - 3(10) = 37 - 30 = 7

3 standard deviations to the right of the mean = 37 + 3(10) = 37 + 30 = 67

We can see that the percentage of lightbulb replacement requests numbering between 37 and 67 falls within 3 standard deviations to the right of the mean. This is just half of the area covered by 99.7%. Thus

The percentage of lightbulb replacement requests numbering between 37 and 67

= 99.7/2 = 49.85%