Question

Suppose that diameters of a new species of apple have a bell-shsped distribution with a mean of 7.2 cm and a standard deviation of 0.38 cm what percentage of the apples have diameters that are between 6.44 cm and 7.96 cm? 

Answer 1

Solution:- 95% of the apples have diameters that are between 6.44 cm and 7.96 cm.

Mean = 7.2, S.D = 0.38

x₁ = 6.44

x₂ = 7.96

By applying normal distruibution:-

$z = \frac{x-\mu }{\sigma }$

z₁ = 2.0

z₂ = -2.0

According to empirical rule 95% of the values in the distribiution lies between 2 standard deviations.