Question

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?

Answer 1

Answer:

217

Step-by-step explanation:

Answer 2

Answer:

We need at least 217 compact fluorescent light bulbs

Step-by-step explanation:

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

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.005 = 0.995$, so $z = 2.575$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ 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 $M = 175, \sigma = 1000$

So

$M = z*\frac{\sigma}{\sqrt{n}}$

$175 = 2.575*\frac{1000}{\sqrt{n}}$

$175\sqrt{n} = 2575$

$\sqrt{n} = \frac{2575}{175}$

$\sqrt{n} = 14.71$

$\sqrt{n}^{2} = (14.71)^{2}$

$n = 216.5$

We need at least 217 compact fluorescent light bulbs