An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. if a sample of 30 bulbs has an average life of 780 hours, how large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?

A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin M as such

In which is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

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step-by-step explanation:

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