Question

Fluorescent lighbulbs have lifetimes that are normally distributed with a mean of 5.2 years and a standard deviation of 1 years.

The figure below shows the distribution of lifetimes of fluorescent lightbulbs.
Calculate the probability that a randomly chosen Fluorescent lighbulb lifetime will be between 3.2 and 6.2.

Answer 1

Explanation:

To solve this problem, we need to standardize the values using z-scores and then find the area under the standard normal distribution curve between those z-scores.

First, we need to find the z-scores for the values 3.2 and 6.2 using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For x = 3.2:

z = (3.2 - 5.2) / 1 = -2

For x = 6.2:

z = (6.2 - 5.2) / 1 = 1

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. The area represents the probability of a randomly chosen Fluorescent lighbulb lifetime being between 3.2 and 6.2.

Using a standard normal distribution table, we can find that the area between z = -2 and z = 1 is approximately 0.8186.

Therefore, the probability that a randomly chosen Fluorescent lighbulb lifetime will be between 3.2 and 6.2 is approximately 0.8186 or 81.86%.