SOLUTION: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.5 years, and standard deviation of 0.6 years.
If 6 items are picked at random, 7% of
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If 6 items are picked at random, 7% of
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Question 1147748: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.5 years, and standard deviation of 0.6 years.
If 6 items are picked at random, 7% of the time their mean life will be less than how many years?
Give your answer to one decimal place. Answer by VFBundy(438) (Show Source):
You can put this solution on YOUR website! First, you want to find the standard deviation of the sample. You do this by taking the standard deviation of the population and dividing it by the square root of the number of items in the sample: = 0.6/2.4495 = 0.2449
Since you want to find the number of years where the mean life is in the lowest 7%, you want to go to a z-table and find the z-score that where the area to the left of the curve is closest to 0.07. The z-score that is closest is -1.48.
Now, you want to set up an equation as such:
x - 2.5 = -1.48(0.2449)
x - 2.5 = -0.3625
x = 2.1375
Rounded off to one decimal point, the answer is 2.1 years.
