Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.43cm and a standard deviation

Question

2 years ago

15

of 0.35cm. Using the empirical rule, what percentage of the apples have diameters that are between 7.08cm and 7.78cm

1 answer:

malfutka [58] · Answer 1 · 2022-09-07T07:45:52+03:00

Answer:

Approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

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

Approximately 95% of the measures are within 2 standard deviations of the mean.

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

In this problem, we have that:

Mean of 7.43cm, standard deviation of 0.35cm.

What percentage of the apples have diameters that are between 7.08cm and 7.78cm?

7.43 - 0.35 = 7.08 cm.

7.43 + 0.35 = 7.778 cm.

Within 1 standard deviation of the mean, so approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.