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:

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

Answer 2

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

The given parameters are:

$\sigma = 1000$ ---- the population standard deviation

$E =\pm 175$ ---- the margin of error

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

So, the margin of error is calculated using:

$E = z \times \frac{\sigma}{\sqrt n}$

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

So, we have:

$\pm 175 = 2.576 \times \frac{1000}{\sqrt n}$

Multiply both sides by $\frac{\sqrt n}{\pm 175}$

$\sqrt n= 2.576 \times \frac{1000}{\pm 175 }$

This gives

$\sqrt n= \frac{2576}{\pm 175 }$

Divide

$\sqrt n= \pm14.72$

Square both sides of the equation

$n= 216.6784$

Approximate

$n= 217$

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

Read more about margin of error at:

https://brainly.com/question/14396648