4. 46 points DevoreStat9 3.E.017 My Notes Ask Your Teacher A new battery\'s volt

Question

4. 46 points DevoreStat9 3.E.017 My Notes Ask Your Teacher A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 93% of all batteries have acceptable voltages. Let Y denote the number of batteries that must be tested. (a) What is p(2), that is P(Y = 2)? (Round your answer to four decimal places.) p(2) = (b) What is p(3)? [Hint: There are two different outcomes that result in Y = 3 (Round your answer to three decimal places.) p(3) = (c) To have Y = 5, what must be true of the fifth battery selected? O The fifth battery must be an A O The fifth battery must be a U. List the four outcomes for which Y-5. (Enter your answer in set notation.) Determine p(5). (Round your answer to five decimal places.) p(5) = (d) Use the pattern in your answers for parts (a)-(c) to obtain a general formula for p(y) p(y) Need Help?eiTalk to Tuter

Explanation / Answer

Solution-

Let Y be the random variable of the number of batteries to be tested to get two batteries which are acceptable.

Then Y must follow negative binomial random variable with parameters number of successes (k) = 2 and probability of success (p)= 0.93

(a) P(2) = 1c1 * 0.93 * 0.07^0 * 0.93

= 0.8649

(b) P(3) = 2c1 * 0.93^1 * 0.07^1 * 0.93

= 0.1211

(c) when Y = 5, then fifth battery must be acceptable.

(d) outcomes when Y=5,

P(5) = 4c1 * 0.93^1 * 0.07^3 * 0.93

= 0.001187

(d) P(y) = (y-1)c1 * 0.93^2 * 0.07^(y-2)

Answers

TY!

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