Probability Aryannah Desty

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 Rank_ . 2) The area in a distribution can be divided into four equal parts called _quartile_ . 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*100/24 p=400/24 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): 25/350 = 1/14 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: 0.367 b Answer: 0.005 c Answer: 0.089 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: 0.2177 Work (describe your process here): I used the table to find this value by looking at the tail of the proportion 10-b) % below this z score (in the body): Answer: 0.7823 Work (describe your process here): I used the table to find this value by looking at the body of the proportion 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 = 0.647 11-b) 19% Answer: p = 0.19 11-c) 4% Answer: p = 0.04 11-d) 5.7% Answer: p =0.057 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: I would not recommend this client for further evaluation anxiety treatment. Explanation: Because this client below the cut off of Z-scores that would required further evaluation for treatment. 12b) z = +2.43 Answer: I would recommend this client to be evaluated for anxiety treatment. Explanation: Because this client above the cut off of Z-scores that would required further evaluation for treatment. 13 ) Imagine a class of 16 fourteen-year-old boys that is treated as a population. The mean height of the boys is m = 67.5 inches with a standard deviation of s = 0.5 inches. Page 2 of 3