Question

the physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 52 and a standard deviation of 7. using the empirical rule rule, what is the approximate percentage of lightbulb replacement requests numbering between 38 and 52? do not enter the percent symbol.

Answer 1

47.5% between 38 and 52 requests for new lightbulbs have been made.

Given,

The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs.

The mean of the distribution, μ = 52

Standard deviation, σ = 7

We have to find the  approximate percentage of lightbulb replacement requests numbering between 38 and 52 using empirical rule;

Here,

z score corresponding to 38 and 52

z score = (x - μ) / σ = (38 - 52) / 7 = -2

Now,

z score corresponding to 52

z score = 52 -52 / 7 = 0/7 = 0

We are aware that, in accordance with the empirical rule, 68% of the data are within one standard deviation of the mean and 95% are within two.

By comparing the z-scores of data point 38 and 52, we can observe that data point 38 is at the mean. 38 is therefore -2 standard deviations above the mean. That is -2σ to 2σ

The center of the normal distribution curve is known to be the mean. Therefore, we will divide 95% by 2 to obtain the percentage of data points 2 SD above the mean.

95/2 = 47.5%

As a result, 47.5% between 38 and 52 requests for new lightbulbs have been made.

Learn more about standard deviation here;

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