It is known that 90% of all brand A zip drives work in a satisfactory manner thr

Question

It is known that 90% of all brand A zip drives work in a satisfactory manner throughout the warranty period (are "successes"). Suppose that n = 10 drives are randomly selected. Let X = t number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic. [Hint: One possible value XIn is .3, corresponding to X3. What is the probability of this value (what kind of random variable is X)?] (Give answers accurate to 3 decimal places.) 4 9 10 x/n p(x/n) Find the mean and variance for XIn from its sampling distribution mean ariance You may need to use the appropriate table in the Appendix af Tables to answer this question.

Explanation / Answer

Solution:-

mean = = xp(x) = 90001/10000 = 9.000

sd = = sqrt((x^2p(x)) ^2) = 0.948

x 0 1 2 3 4 5 6 7 8 9 10 x/n 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p(x/n) 0.0000 0.0000 0.0000 0.0000 0.0001 0.0015 0.0112 0.0574 0.1937 0.3874 0.3487

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