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zzz [600]
3 years ago
14

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.4 years, and standard deviation of

0.6 years. The 4% of items with the shortest lifespan will last less than how many years?
Mathematics
1 answer:
QveST [7]3 years ago
3 0

Answer:

7.35 years

Step-by-step explanation:

Given that :

mean = 8.4

standard deviation = 0.6

From the negative z tables, the corresponding data for 0.04 = -1.75

So, using the z-score formula:

z = \dfrac{x  - \mu}{\sigma}

-1.75 = \dfrac{x - 8.4}{0.6}

-1.75 × 0.6  = x - 8.4

- 1.05 = x - 8.4

x = -1.05 + 8.4

x =  7.35 years

the shortest lifespan will last less than 7.35 years

∴ the longest 4% will have lifespans longer than x = 8.4 + 1.75(0.6)

= 9.45 years

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