Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11 years, and standard deviation of 1.9 years.

The 4% of items with the shortest lifespan will last less than how many years

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Answer 1

Here given Mean = 11 years

Standard deviation = 1,9 years

We need to less than how many years does the 4% of items with the shortest lifespan will last

Here given proportion of items, p-value = 0.04

The z-score that has an area of 0.04 to its left is -1.75069 from the online p-value to z-score calculator

We know that

Z-score = (X - ) /

-1.75069 = (X - 11) / 1.9

X - 11 = 1.9 * (-1.75069)

X - 11 = -3.32631

X = 11 - 3.32361

X = 7.673689

So The 4% of items with the shortest lifespan will last less than 7.6737 years rounded to 4 decimal places