Probability Template

PSYC 354 P ROBABILITY T EMPLATE Questions 1-5 Fill in the highlighted blanks to answer/complete the statements. Use the textbook as your resource for these definitions. (3 pts each) 1) The particular score associated with a percentile rank is known as a _ Percentile _ . 2) The area in a distribution can be divided into four equal parts called _ Quartiles _ . 3) In independent random sampling, Sampling __ _ With _ _ Replacement _ is the process of returning each individual to the population before making the next selection. 4) Probabilities are expressed within a limited range. The lower limit of the range is _ 0 _ , which indicates an event that never occurs; and the higher limit of the range is _ 1 _ , which indicates an event that always occurs. 5) The _ Unit _ _ Normal _ table lists proportions of the normal distribution for a full range of possible z-score values. Questions 6-9 Complete the following exercises: (2 pts each) 6) What is the probability of hitting a target if, in the long run, 4 out of every 24 attempts actually hit the target? (3 pts) Answer (show work): P = 4/24 P = 0.1667 P = 16.67% 7) On a TV game show, 25 people have won the grand prize and a total of 350 people have competed. Estimate the probability of winning the grand prize. (3 pts) Answer (show work): P = 25/350 P = .0714 P = 7.14% 8) Convert the following decimals to percentages : (2 pts each) a) 0.65 b) .832 c) .07 a) Answer 65% b) Answer 83.2% c) Answer 7% 9) Convert the following a) Answer .367 b) Answer .005 c) Answer .089 Page 1 of 3

PSYC 354 percentages to decimals : (2 pts each) a) 36.7% b) 0.5% c) 8.9% 10) Using the z table in Appendix B (Table B-1), calculate the following percentages for a z score of +0.78. Describe how you used the table to find these values. (4 pts each for a and b) 10-a) % above this z score (in the tail): Answer: .2177 or 21.77% Work (describe your process here): I located the unit normal table in Appendix B of my textbook. I searched for the Z-score of +0.78 in column A. Once I located the z-score I followed the row across to column C (Proportion in tail) and located the proportion of .2177. Then I changed the proportion to a percentage of 21.77% 10-b) % below this z score (in the body): Answer: .7823 or 78.23% Work (describe your process here): I located the unit normal table in Appendix B of my textbook. I searched for the Z-score of +0.78 in column A. Once I located the z-score I followed the row across to column B (Proportion in body) and located the proportion of .7823. Then I changed the proportion to a percentage of 78.23% 11) Rewrite each of the following percentages as probabilities, or p -values, which are expressed in decimal format: (2 pts each) 11-a) 64.7% Answer: p = .6470 11-b) 19% Answer: p = .1900 11-c) 4% Answer: p = .0400 11-d) 5.7% Answer: p = .0570 12) A certain clinical measure of anxiety has a cut-off of z = +2.14, meaning that z-scores higher than this indicate severe levels of anxiety that may require treatment. Two of your clients have the z-scores listed below. Based on the given score and the information here, would you recommend that the client be further evaluated for anxiety treatment? Explain your reasoning. Evaluate each client independently. (3 pts each) 12a) z = -1.37 Answer: No, further evaluation would not be recommended. Explanation: I would not recommend further evaluation for this client because his/her z- Page 2 of 3