Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.3 years, and standard deviation of 2.7 years.

If 10 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 #1

Let , , n=10

Now , the sampling distribution of the sample mean is approximately normally distributed with sample mean and sample standard deviation

We have ,

...............(I)

From standard normal distribution table, ...............(II)

From (I) and (II) , we get ,

Therefore ,

If 10 items are picked at random, 7% of the time their mean life will be less than 8.04 years.

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Give your answer to one decimal place.

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If 20 items are picked at random, 6% of the time their mean life
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Give your answer to one decimal place.

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QUESTION PART A: A manufacturer knows that their items have a
normally distributed lifespan, with a mean of 6.6 years, and
standard deviation of 0.8 years.
If 22 items are picked at random, 6% of the time their mean life
will be less than how many years?
Give your answer to one decimal place.
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distributed, with a mean of 679 grams and a standard deviation of
19 grams.
If you pick...

A manufacturer knows that their items have a normally
distributed lifespan, with a mean of 10.3 years, and standard
deviation of 2.4 years. The 10% of items with the shortest lifespan
will last less than how many years? Give your answer to one decimal
place.

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