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VashaNatasha [74]
3 years ago
13

If a light bulb manufacturing company wants to​ estimate, with 99​% ​confidence, the mean life of compact fluorescent light bulb

s 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?
Mathematics
2 answers:
matrenka [14]3 years ago
6 0

Answer:

217

Step-by-step explanation:

Reptile [31]3 years ago
4 0

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

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