Question

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.5 ounces, What is the probability that a randomly selected item from the production will weigh at least 4.25 ounces?

Answer 1

To find the probability of a randomly selected item weighing at least 4.25 ounces, we need to calculate the z-score and use a z-table or calculator to find the probability associated with it. The probability is 0.6915, or 69.15%.

Step-by-step explanation:

To solve this problem, we need to use the normal distribution and the given mean and standard deviation. Let's calculate the z-score for the weight of 4.25 ounces:

Z = (X - μ) / σ

Plugging in the values, we have:

Z = (4.25 - 4.5) / 0.5 = -0.5

We can then use a z-table or a calculator to find the probability associated with this z-score. The probability of a randomly selected item weighing at least 4.25 ounces is the complement of the probability of it weighing less than 4.25 ounces. We can find this probability by subtracting the probability of the left tail from 1. Using the z-table or a calculator, we find that the probability of the left tail is 0.3085. Therefore, the probability of a randomly selected item weighing at least 4.25 ounces is 1 - 0.3085 = 0.6915, or 69.15% (rounded to two decimal places).