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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-08-13T18:58:27+02:00

Answer: 0.9147

Step-by-step explanation:

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

[tex]\mu=14.2\text{ years}[/tex]

[tex]\sigma= 3.8\text{ years}[/tex]

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

z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 9

[tex]z=\dfrac{9-14.2}{3.8}\approx-1.37[/tex]

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

[tex]P(X>9)=P(z>-1.37)=1-P(x\leq-1.37)\\\\=1- 0.0853435\approx0.9146565\approx0.9147[/tex]

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