Question

The diameters of red delicious apples of an orchard have a normal distribution with a mean of 3 inches and a standard deviation of 0.5 inch. What diameter measurement separates the smallest 33% of apples?

Answer 1

Solution :

Given that,  

mean = $\mu$ = 3

standard deviation = $\sigma$ = 0.5

Using standard normal table ,

P(Z < z) =33%

P(Z < -0.44) = 0.33

z = -0.44

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = -0.44 * 0.5 + 3 = 2.78

The diameter measurement separates the smallest 33% of apples 2.78