Mathematics, 16.03.2020 22:24 challenggirl

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?

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Answer from: brapmaster764

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:

link

Answer from: denjayjr681

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 $M = 175, \sigma = 1000$

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

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

$175\sqrt{n} = 2575$

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

$\sqrt{n} = 14.71$

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

n = 216.5

We need at least 217 compact fluorescent light bulbs

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

something over 10 so ? /10

step-by-step explanation:

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If a light bulb manufacturing company wants to estimate, with 99% confidence, the mean life of compa...