If a light bulb manufacturing company wants to estimate, with 99% confidence, the mean life of compact fluorescent light bulbs to within plus or minus175 hours and also assumes that the population standard deviation is 1000 hours, how many compact fluorescent light bulbs need to be selected?

The number of compact fluorescent light bulbs that needs to be selected is 217

The given parameters are:

---- the population standard deviation

---- the margin of error

At 99% confidence interval, the z value is 2.576.

So, the margin of error is calculated using:

Substitute values for the margin of error (E) and the standard deviation ().

So, we have:

Multiply both sides by

This gives

Divide

Square both sides of the equation

Approximate

Hence, the number of compact fluorescent light bulbs that needs to be selected is 217

Read more about margin of error at:

link

We need at least 217 compact fluorescent light bulbs

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 M as such

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

How many compact fluorescent light bulbs need to be selected?

We need at least n bulbs, in which n is found when

So

We need at least 217 compact fluorescent light bulbs

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation: