Question

The following graph portrays the distribution of the number of spicy chicken sandwiches sold at a nearby Wendy's for the last 141 days.
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67. (Round your answers to 2 decimal places.)

If we use the Empirical Rule, on 68 percent of the days sales will be between

95 percent of the days sales will be between

Answer 1

68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

What is the empirical rule?

If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.

We have:

The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.

As we know, from the empirical rule, 68% of the data will lie in one standard deviation of the mean, i.e., in the interval with the endpoints x±s

for samples and with endpoints u±б for the population.

x = 91.9

s = 4.67

x - s = 91.9 - 4.67 = 87.23

x + s = 91.9 + 4.67 = 96.57

68% of the day's sales will be between 87.23 and 96.57

95% of the data will lie within two standard deviations of the mean, which means in the interval with the endpoints  x±2s for samples and with endpoints  u±б population.

x - 2s = 82.56

x + 2s = 101.24

On 95% of the days, sales will be between 82.56 and 101.24

Thus, 68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

Learn more about the empirical rules here:

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