can someone help me with 8,9,11 and 13 c. Compare the results from parts (a) and

Question

can someone help me with 8,9,11 and 13

c. Compare the results from parts (a) and (b) cpiaced berbre the second item is selected. d. Given a choice between selecting with replacement and selecting without replace- ment, which choice makes more sense in this situation? Why ng Hunter Orange A study of hunting injuries and the wearing of "hunter" or ange clothing showed that among 123 hunters injured when mistaken for game, 6 were wearing orange (based on data from the Centers for Disease Control). If a low-up study begins with the random selection of hunters from this sample of 123 find the probability that the first two selected hunters were both wearing orange a. Assume that the first hunter is replaced before the next one is selected. b. Assume that the first hunter is not replaced before the second hunter is selected. c. Given a choice between selecting with replacement and selecting without replac e- ment, which choice makes more sense in this situation? Why? 9. Probability and Guessing A psychology professor gives a surprise quiz consisting of 10 true/false questions, and she states that passing requires at least 7 correct re sponses. Assume that an unprepared student adopts the questionable strategy guessing for each answer a. Find the probability that the first 7 responses are correct and the last b. Is the probability from part (a) equal to the probability of passing? Why or why 3 are wrong not? 10. Selecting U.S. Senators In the 107th Congress, the Senate consists of 13 women and 87 men. If a lobbyist for the tobacco industry randomly selects three different sena tors, what is the probability that they are all women? Would a lobbyist be likely to use random selection in this situation? 11. Coincidental Birthdays a. The author was born on November 27. What is the probability that two other ran domly selected people are both born on November 27? (Ignore leap years.) b. What is the probability that two randomly selected people have the same birthday? (Ignore leap years.) 12. Coincidental Birthdays a. One couple attracted media attention when their three children, born in different years, were all born on July 4. Ignoring leap years, find the probability that three randomly selected people were all born on July 4. Is the probability low enough so such an event is not likely to occur somewhere in the United States over the course of several years b. Ignoring leap years, find the probability that three randomly selected people all have the same birthda tance Sampling With one method of a procedure called acceptance sam a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The Niko Electronics Com pany has just manufactured 5000 CDs, and 3% are defective. If 12 of these CDs are randomly selected for testing, what is the probability that the entire batch will be 13 cce accepted?

Explanation / Answer

9) Given that,

there are 10 true false questions and passing requires atleast 7 questions correct.

Here we have to find probability that the first 7 responses are correct and last three are wrong.

Probability = (1/2)^7 * (1/2)^3 = 0.0010

For passing we have to calculate P(X >= 7)

Here we can find probability using binomial distribution.

X = number of questions are correct.

X has binomial distribution with parameter n = 10, p = 0.5

X has pmf,

P(X = x) = (10 C x) * 0.5x * 0.510-x

P(X >= 7)= P(X=7) + P(X=8) + P(X=9)+P(X=10)

= 0.1172 + 0.0439 + 0.0098 + 0.0010 = 0.1719

We can see that both probabilities are different.

In first probability there are less chances of correcting first seven questions are correct.

WHile in the second probability there are more chances than first to correct atleast 7 questions are correct among 10.

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