Question

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.

Answer 1

`2.7`

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:

`\begin{gathered} Z=(X-\mu)/(\sigma) \\ -1.282=(X-3.5)/(0.6) \\ X=2.73\approx2.7 \end{gathered}`

Thus, this is the answer: 2.7 years