Question

the weight of oranges growing in an orchard is normally distributed with a mean weight of 5 oz. and a standard deviation of 1.5 oz. what is the probability that a randomly selected orange from the orchard weighs less than 4 oz., to the nearest thousandth?

Answer 1

0.251

Explanation:

for a normal distribution question, we need to use the z-score formula for finding the area (probability).

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (4 - 5) / 1.5

= -0.67

in the z-table, find -0.6 down the side column and 0.07 on the top row. the number in the table where these two meet is 0.25143. this is the area to the left of z = -0.67. this is what we want for this question since we want an orange that weighs less than 4oz.

that means that the probability is 0.251 to nearest thousandth