Question

The average lifetime of a smoke detector is 5 years, or 60 months, and the standard deviation of lifetimes is 8 months. The lifetime of individual smoke detector units is a distribution that is right-skewed.

A.) Using units of months, determine the sampling distribution of the sample mean for samples of size 200 smoke detectors.

B.) Repeat part a. for sample size of 500.

C.) Why can you still answer part a. and b. when the distribution of smoke detector lifetimes is not normal, but right-skewed?

D.) What is the probability that the sampling error made in estimating the population mean lifetime by the mean lifetime of a simple random sample of 200 detectors will be at most 1?

E.) Repeat part d. for sample size of 500.

Answer 1

solution: M= 60 months = 8 months (A ~ Normal distribution. E (I) = = 60 (B) À ~ Normal distribution E(x) = 1=60 Z = X-M (d, pa

e Even if the distribution of population is right skewed, the distribution of samble mean will be abproximately mormal because sample size is large enough [ By central limity theorem

o.566 (d, p (1x-41 -1) = P(= 1 cz co 566) = P(-1.77 C221077) = 10.9233 © P(Ix-|51) PI -L ezcoast) = P(-2-99 cz (279) ={0.9947 -ul < Z 0 358