Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.2 years, and standard deviation of 3.8 years. If you randomly purchase one item, what is the probability it will last longer than 9 years?

Answer 1

Answer: 0.9147

Explanation:

Explanation:

Given : A manufacturer knows that their items have a normally distributed lifespan with

`\mu=14.2\text{ years}`

`\sigma= 3.8\text{ years}`

Let x be the random variable that represents the lifespan of items.

z-score :
`z=(x-\mu)/(\sigma)`

For x= 9

`z=(9-14.2)/(3.8)\approx-1.37`

Now by standard normal distribution table, the probability it will last longer than 9 years will be :-

`P(X>9)=P(z>-1.37)=1-P(x\leq-1.37)\\\\=1- 0.0853435\approx0.9146565\approx0.9147`

Hence, the probability it will last longer than 9 years = 0.9147