Question

Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.45cm and a standard deviation of 0.4cm. Using the empirical rule, what percentage of the apples have diameters that are greater than 7.85cm? Please do not round your answer.

Answer 1

The percentage is 68.26%

Explanation:

Before we use the empirical rule , we need to find the value of the z-score

Mathematically;

z-score = (x - mean)/SD

Thus;

z-score = (7.85 - 7.45)/0.4 = 0.4/0.4 = 1

So the percentage we want to calculate now is the percentage of values within 1 standard deviation of the mean

According to the empirical rule, 68.26% of values are within 1 standard deviation of the mean