Question

The shelf life of a particular dairy product is normally distributed with a mean

of 14 days and a standard deviation of 2 days. Draw the probability density
function to help you answer the following. Do not use the z-table/
About what percent of the products last between 12 and 16 days?
About what percent of the products last between 14 and 18 days?
About what percent of the products last IO days or less?
About what percent of the products last 16 days or more?
About what percent of the products last 20 days or longer?

Answer 1

To find the percentage of products that last between 12 and 16 days, we need to find the area under the probability density function (PDF) curve between these two values. We can use the z-score formula to convert the values to their corresponding z-scores.

Step-by-step explanation:

To find the percentage of products that last between 12 and 16 days, we need to find the area under the probability density function (PDF) curve between these two values. We can use the z-score formula to convert the values to their corresponding z-scores. The z-score formula is given by z = (x - mean) / standard deviation.

In this case, the mean is 14 and the standard deviation is 2. So, for 12 days, the z-score would be (12 - 14) / 2 = -1. For 16 days, the z-score would be (16 - 14) / 2 = 1.

Now, we can use a standard normal distribution table (or a calculator) to find the corresponding probabilities. The area under the curve between -1 to 1 represents the percentage of products that last between 12 and 16 days.