Answered

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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.5 years, and standarddeviation of 0.6 years.The 10% of items with the shortest lifespan will last less than how many years?[1])])1)Give your answer to one decimal place.

Sagot :

[tex]2.7[/tex]

1) In this question, we need to make use of a standard normal table to check which is the value (in terms of Z-score) for that 10%.

2) Checking that out, we can see that the Z-score is -1.282. So now, let's plug that into the Z-score formula so that we get the corresponding raw value:

[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ -1.282=\frac{X-3.5}{0.6} \\ X=2.73\approx2.7 \end{gathered}[/tex]

Thus, this is the answer: 2.7 years

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