The lifespan of a 100-W fluorescent lamp is define to be normally distributed with displaystylesigma={30} hrs. A random sample of 15 lamps has a mean life of displaystyle{x}={1000} hours. Construct a 90% lower-confidence bound on the mean life.

remolatg

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

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 x±za2σn. Where 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 xzασn.
Step 2
The 90% lower-confidence bound on the mean life is given below:
μzασn
10001.283015
10001.28×7.746
10009.9149
990.1
Thus, the 90% lower-confidence bound on the mean life is 990μ.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-27Added 2605 answers

Answer is given below (on video)

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