Question

a manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.7 years, and standard deviation of 1.5 you randomly purchase one item, what is the probability it will last longer than 16 years?

Answer 1

the probability an item will last longer than 16 years with a mean lifespan of 11.7 and standard deviation of 1.5, is 0.002052.

Step-by-step explanation:

To calculate the probability that an item with a normally distributed lifespan will last longer than 16 years when it has a mean of 11.7 years and a standard deviation of 1.5 years, we use the z-score formula.

The z-score formula is z = (X - μ) / σ, where X is the value of interest (16 years), μ is the mean, and σ is the standard deviation.

Applying the values we have: z = (16 - 11.7) / 1.5

= 2.87.

Next, we look up the z-score in a standard normal distribution table or use a calculator with statistical functions to find the probability associated with a z-score of 2.87.

z= 0.002052