Question

The weights of items produced by a company are normally distributed with a mean of 5 ounces and a standard deviation of 0.2 ounces. What percentage of the items weighs less than 4.4 ounces (i.e., P(X < 4.4))?

Answer 1

The percentage of the items that weigh less than 4.4 ounces (i.e., P(X < 4.4) is 0.135%

Explanation:

This is a normal distribution problem with

Mean = 5 ounces

Standard deviation = 0.2 ounces

To find the percentage of the items that weigh less than 4.4 ounces (i.e., P(X < 4.4),

We will use the normal distribution table.

First of, we standardize or normalize 4.4

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (4.4 - 5)/0.2 = -3.0

To determine the percentage of the items that weigh less than 4.4 ounces

P(x < 4.4) = P(z < -3.0)

We'll use data from the normal probability table for these probabilities

P(x < 4.4) = P(z < -3.0) = 0.00135

In percentage, this is 0.135%

Hope this Helps!!!