1. 2.13/6 points | Previous Answers Dovorestats 3.E.069 My Notes Lach of 12 refr

Question

1. 2.13/6 points | Previous Answers Dovorestats 3.E.069 My Notes Lach of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 7 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X he the number among the first 6 examined that have a defeclive cormpressor (a) Calculate Pix - 4) and P(X 4), (Round your answers to four decimal placcs.) P(X-4)0.3728 Px s 4)-08788 (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) 0010 B919 : (c) Consider a large shipment ot 400 refrigerators, af which 40 have defective compressors. It X is the number among 15 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) PX 3) than to use the hypergeometric pmf We can approximate the hypergeometric distribution with the binomial and o-M/N-7/12 Approximate P(X S3) using that method. (Round your answer to three decimal pleces.) PXS 3) 0.490 distribution if the population size and the number of successes are large. Here n-6 You may need to use the appropriate table in the Appendix of Tables to answer this question Need Help?Ret Taik to a Tuter

Explanation / Answer

c)

here n = 15

p = 40/ 400 = 0.1

using R

pbinom(3, size=15, prob=0.1)

P(X <= 3 ) = 0.94444

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