Show all workings for both questions, unless stated otherwise. Question 1 Lifeti

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Show all workings for both questions, unless stated otherwise.

Question 1     Lifetime

A factory produces lightbulbs that have a lifespan which is left-skewed with a mean of 1000 hours and a standard deviation of 39 hours. The factory needs to keep an eye on the production process to ensure that everything is working properly and that lightbulbs produced meet the advertised standard. This is done by testing the lifespans of a random sample of 36 in order to test the process.

(a) Describe the sampling distribution of the sample mean lifetime of lightbulbs.

(b) If the process is working correctly, what is the probability that the sample will produce a mean of less than 990 hours?

(c) Explain why we cannot determine the probability that a random sample of 10 lightbulbs has a mean lifespan less than 990 hours.

Explanation / Answer

here as sample size is greater then 30,

sampling distribution will be approximately normal with mean =1000

and std error =std deviation/(n)1/2 =6.5

b) P(X<990) =P(Z<(990-1000)/6.5) =P(Z<-1.5385)=0.062

c) as we do not know if parent distribution is normal and as sample size is less then 30 we can not assume that to be approximately normal too

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