Question

The maintenance department at the main campus of a large state university receives daily requests to replace fluorecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 63 and a standard deviation of 5. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 53 and 63?

Answer 1

Mean = 63

Standard deviation = 5

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

63 - 2x5 = 53

63 + 2x5 = 73

53 is 2 standard deviations below mean

73 is 2 standard deviations above mean

95% of data values are between 53 and 73

Since the distribution is symmetric about the mean,

95/2 = 47.5% of values are between 53 and 63 and 47.5% are between 63 and 73.

Therefore, percentage of lightbulb replacement requests numbering between 53 and 63 = 47.5%