Question

Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.25 cm and a standard deviation of 0.42 cm. Using the empirical rule, what percentage of the apples have diameters that are between 6.41cm and 8.09 cm?

Answer 1

Answer:

95%

Step-by-step 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:

$N_U=\frac{U-M}{SD} =\frac{8.09-7.25}{0.42}=2 \\N_L=\frac{M-L}{SD} =\frac{7.25-6.41}{0.42}=2$

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.