We have an answer to "The lifespan of a 100-W fluorescent lamp is..."

remolatg

Answered question

2021-02-09

The lifespan of a 100-W fluorescent lamp is define to be normally distributed with

σ = 30

hrs. A random sample of 15 lamps has a mean life of

x = 1000

hours.
Construct a

90 %

lower-confidence bound on the mean life.

Answer & Explanation

Lacey-May Snyder

Skilled2021-02-10Added 88 answers

Step 1
The confidence interval for mean when the population standard deviation is known, is given by $\overset{―}{x} \pm z_{\frac{a}{2}} \frac{σ}{\sqrt{n}}$ . Where $\overset{―}{x}$ is the sample mean which is given as 1000 hours, $σ$ is population standard deviation which is given as 30 hours, n is sample size which is 15 lamps and z value depends on the confidence level and for $90 %$ it is 1.28. For lower bound use $\overset{―}{x} - z_{α} \frac{σ}{\sqrt{n}} .$
Step 2
The 90% lower-confidence bound on the mean life is given below:
$μ \geq - z_{α} \frac{σ}{\sqrt{n}}$
$\geq 1000 - 1.28 \frac{30}{\sqrt{15}}$
$\geq 1000 - 1.28 \times 7.746$
$\geq 1000 - 9.9149$
$\geq 990.1$
Thus, the $90 %$ lower-confidence bound on the mean life is $990 \leq μ .$

Jeffrey Jordon

Expert2021-10-27Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Didn't find what you were looking for?