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15 votes
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.8 years, and standard deviation of 1.7 years. The 10% of items with the shortest lifespan will last less than how many years?

User Janniks
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1 Answer

15 votes
15 votes

Answer:

3.6 years

Explanation:

Using the standard normal probability distribution table, we obtain the Zscore which is 10% to left of the distribution.

The Zscore gives, - 1.282

To obtain the number of years, let this be x ;

Recall, the Zscore formula :

Zscore = (x - μ) / σ

x = number of years

μ = 5.8

σ = 1.7

Zscore = (x - μ) / σ

-1.282 = (x - 5.8) / 1.7

-1.282 * 1.7 = x - 5.8

-2.1794 = x - 5.8

-2.1794 + 5.8 = x

x = 3.6206

x = 3.6 years

User Kyle Chadha
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