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 10. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 63 and 83

47.5% of lightbulb replacement requests numbering between 63 and 83

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 63

Standard deviation = 10

What is the approximate percentage of lightbulb replacement requests numbering between 63 and 83

63 is the mean

83 = 63 + 2*20

So 83 is two standard deviations above the mean.

The normal distribution is symmetric, so 50% of the measures are above the mean and 50% below the mean.

Of those above the mean, 95% are within 2 standard deviations of the mean.

So

0.5*95% = 47.5%

47.5% of lightbulb replacement requests numbering between 63 and 83

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: