A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.2 years, and standard deviation of

Question

3 years ago

9

3.8 years. If you randomly purchase one item, what is the probability it will last longer than 9 years?

1 answer:

arsen [322] · Answer 1 · 2022-06-07T01:22:58+03:00

Answer: 0.9147

Step-by-step 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 : $z=\dfrac{x-\mu}{\sigma}$

For x= 9

$z=\dfrac{9-14.2}{3.8}\approx-1.37$

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