Question

Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.42cm and a standard deviation of 0.36cm. Using the empirical rule, what percentage of the apples have diameters that are between 7.06cm and 7.78cm?

Answer 1

In statistics, the 68–95–99.7 rule, also known as the empirical rule tells us that 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

The following information has been provided:

We need to compute :

The corresponding z-values needed to be computed are:

Therefore, we get:

Using the empirical rule 68.27% of the values lie within one standard deviation of the mean.

The following is obtained graphically:

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