Question

Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 56 hours and a standard deviation of 3.2 hours. With this​information, answer the following questions.​

What proportion of light bulbs will last more than 6262 hours?​

Answer 1

To find the proportion of light bulbs that will last more than 62 hours, calculate the z-score using the mean and standard deviation, then use a standard normal distribution table or calculator to find the proportion to the right of the z-score.

Step-by-step explanation:

To find the proportion of light bulbs that will last more than 62 hours, first we need to calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value we're interested in (62), μ is the mean (56), and σ is the standard deviation (3.2).

Plugging in the values, we get:

z = (62 - 56) / 3.2 = 1.875

Next, we use a standard normal distribution table or calculator to find the proportion to the right of the z-score. In this case, the proportion of light bulbs that will last more than 62 hours is approximately 0.0312, or 3.12%.