Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7 years, and standard deviation of 0.9 years.The 10% of items with the shortest lifespan will last less than how many years?

Answer 1

The 10% of items with the shortest lifespan will last less than approximately 5.848 years.

Step-by-step explanation:

To find the number of years in which the 10% of items with the shortest lifespan will last less than, we need to find the value of the 10th percentile. The formula to calculate the percentile is:

Percentile = mean + z * (standard deviation)

Where z is the z-score corresponding to the desired percentile.

In this case, since we want the 10th percentile, we need to find the z-score for the 10th percentile. We can use a standard normal distribution table or a calculator to find this value. The z-score for the 10th percentile is approximately -1.28.

Substituting the values of mean, standard deviation, and the z-score into the formula:

Percentile = 7 + (-1.28) * 0.9 = 7 - 1.152 = 5.848

Therefore, the 10% of items with the shortest lifespan will last less than approximately 5.848 years.