Reference no: EM133196982

Topic - Probability and Standardized Scores

Assignment 1: Finding Scores

DQ1: The process of random sampling guarantees that the sample selected will be representative of the population. Why is this statement not true? What other factors and variables influence the outcomes of studies?

DQ2: Assignment Probability Project

The following statements are all incorrect. Explain the statements and the errors fully using the probability rules discussed in topic two.

1. The number 7 is a lucky number so you are more likely to win raffles with ticket number 7 than with a different number.

2. I roll two dice and add the results. The probability of getting a total of 8 is 1/12 because there are 12 different possibilities and 8 is one of them.

3. Mr. Verde has to have a major operation. Ninety-three percent of the people who have this operation make a complete recovery. There is a 93% chance that Mr. Verde will make a complete recovery if he has this operation.

4. The Ramblers play the Chargers. The Ramblers can win, loose, or draw, so the probability that they win is 1/3.

5. I have flipped an unbiased coin four times and got heads. It is more likely to get tails the next time I flip it.

6. Thirty random college students are asked if they study during the week. Since 60% said yes, a statement can be made that 40% of students only study on the weekend.

7. I have two coins. If I flip them together, the probability of getting a heads and a tails is 1/3. This is because you can only get two heads, two tails, or one head and one tail.

Assignment 2: Finding Scores

a. the upper 2 percent, that is, 2 percent to the right (and 98 percent to the left)?

b. the lower 10 percent?

c. the upper 60 percent?

d. the middle 95 percent? [Remember, the middle 95 percent straddles the line perpendicular to the mean (or the 50th percentile), with half of 95 percent, or 47.5 percent, above this line and the remaining 47.5 percent below this line.]

e. the middle 99 percent?

5.14 For the normal distribution of burning times of electric light bulbs, with a mean equal to 1200 hours and a standard deviation equal to 120 hours, what burning time is identified with the

a. upper 50 percent?

b. lower 75 percent?

c. lower 1 percent?

d. middle 90 percent?

Chapter 8, numbers 8.16 and 8.19 -

8.16 A traditional test for extrasensory perception (ESP) involves a set of playing cards, each of which shows a different symbol (circle, square, cross, star, or wavy lines). If C represents a correct guess and I an incorrect guess, what is the probability of

a. C?

b. CI (in that order) for two guesses?

c. CCC for three guesses?

d. III for three guesses?

8.19 sensor is used to monitor the performance of a nuclear reactor. The sensor accurately reflects the state of the reactor with a probability of .97. But with a probability of .02, it gives a false alarm (by reporting excessive radiation even though the reactor is performing normally), and with a probability of .01, it misses excessive radiation (by failing to report excessive radiation even though the reactor is performing abnormally).

a. What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss?

b. To reduce costly shutdowns caused by false alarms, management introduces a second completely independent sensor, and the reactor is shut down only when both sensors report excessive radiation. (According to this perspective, solitary reports of excessive radiation should be viewed as false alarms and ignored, since both sensors provide accurate information much of the time.) What is the new probability that the reactor will be shut down because of simultaneous false alarms by both the first and second sensors?

c. Being more concerned about failures to detect excessive radiation, someone who lives near the nuclear reactor proposes an entirely different strategy: Shut down the reactor whenever either sensor reports excessive radiation. (According to this point of view, even a solitary report of excessive radiation should trigger a shutdown, since a failure to detect excessive radiation is potentially catastrophic.) If this policy were adopted, what is the new probability that excessive radiation will be missed simultaneously by both the first and second sensors?