Sampling Distributions Show all workings. Graph or table is needing for each Que

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Sampling Distributions

Show all workings. Graph or table is needing for each Questions.

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 (X bar). (You may need to draw a Pivot table & Clustered Column Chart)

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

(c) What are the upper and lower boundaries of the middle 80% of the sample mean lifetime (X bar)

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

Explanation / Answer

(d) SAMPLE size<30; we cant use z-score

Excel formula:

given Mean= 1000 SD= 39 N= 36 X= 990 (b) P(X<x)= 0.398817 (C ) 80% Confidence interval Z SCORE= 1.281552 Std error= 6.5 CI: Lower bound= 991.6699 Upper bound= 1008.33

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