Question

Suppose that the weight of navel oranges is normally distributed with mean =8oz and standard deviation=1.5oz

a. What proportion of oranges weigh less than 5oz?

b. What proportion of oranges weigh between 6.8 and 8.9oz?

Answer 1

Ans (a) It is given that the weights of navel oranges is normally distributed with mean, and standard deviation,

First we have to calculate the corresponding z-score :

given:

So the area below z=-2 is going to be the answer, i.e., it tell the proportion of oranges weigh less than 5 oz.

Using z- table we find the area below z=-2

Or we say that the proportion of oranges weigh less than 5oz is 0.0228 or 2.28%

(b) In this case we need to calculate the proportion of oranges weigh between 6.8oz and 8.9oz, so we need to calculate the two different z-scores, one for 6.8oz and the other for 8.9oz and then the area between these two z-scores is our final answer.

now for, x=8.9

The proportion of oranges weigh between 6.8oz and 8.9oz is 0.5139 or 51.39%