Question

Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.26cm and a standard deviation of 0.43cm. Using the empirical rule, what percentage of the apples have diameters that are less than 8.12cm?

Answer 1

95%

Explanation:

Upper limit = 8.09 cm

Lower limit = 6.41 cm

Distribution mean = 7.25 cm

Standard deviation = 0.42 cm

The number of standard deviations from the mean of the upper and lower limits are, respectively:

Both limits are two standard deviations away from the mean.

According to the empirical rule, in normal distributions, 95% of the data falls within two standard deviations of the mean. Therefore, 95% of the apples have diameters that are between 6.41cm and 8.09 cm.