Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.6 years, and standard deviation of 2.6 years.If you randomly purchase one item, what is the probability it will last longer than 4 years

Answer 1

Explanation

We are given the following information:

`\begin{gathered} mean(\mu)=11.6 \\ standard\text{ }deviation(\sigma)=2.6 \end{gathered}`

We are required to determine the probability that the item purchased will last longer than 4 years.

This is achieved thus:

We know that we can standardize the normal distribution using the formula:

`Z=(X-\mu)/(\sigma)`

Therefore, we have:

`\begin{gathered} P(X>4)=P(Z>(4-11.6)/(2.6)) \\ =P(Z>-2.923) \\ =0.99827 \end{gathered}`

Hence, the answer is:

`\begin{equation*} 0.99827 \end{equation*}`