4 STAT Questions

1.

Roll a fair six-sided die. You win $5 if you roll a 1, you lose $2 if you roll a 5 or a 6, and for any other outcome you win or lose nothing. Complete parts a and b below. a. Complete the table that shows the probability distribution. Win Prob 5 1 6 0 D -2 El (Simplify your answers.) The Empirical Rule applies rough approximations to probabilities for any unimodal, symmetric distribution. But for the Normal distribution we can be more precise, as the figure shows. Use the figure and the fact that the Normal curve is 68% symmetric to answer the questions. Do not use a Normal Density table or technology. Complete parts a through e. 95% K K Almost All Z -2 . . . . . a. Roughly what percentage of z-scores are between - 2 and 2? Almost All 95% 68% 50%Wechsler IQs have a population mean of 100 and a population standard deviation of 15 and are approximately Normally distributed. Use one of the technology outputs below to find the probability that a randomly selected person will have an IQ of 105 or above. State whether Figure (a) or Figure (b) is the correct representation of a person with an IQ of 105 or above. . . . . . Figure (a) Figure (b) Density Density 0.025 0.025 0.02 0.02 0.015 0.015 0.01 0.01 0.005 0.005 60 80 100 120 140 60 80 100 120 140 Y Means 100 Sid. Dev.: 15 Mearc 100 Std Dev- 15 Prob( X > 105 )- 0.63055866 Use to find the probability. Figure (b) Figure (a)Use technology to nd the indicated area under the standard Normal curve. Include an appropriately labelled sketch of the Normal curve and shade the appropriate region. a. Find the probability that a z-score will be 1.92 or less. b. Find the probability that a z-score will be 1.92 or more. c. Find the probability that a z-score will be between 1.4 and - 1.04. .m a. Which graph below shows the probability that a z-score is 1.92 or less? A. B. c. .9 D. a a (if {L}? l; -1 Q? 1 99 -1 Q9 1 Q? . nn . M. The probability that a z-score will be 1.92 or less is D. (Round to four decimal places as needed.) For each question, find the area to the right of the given z-score in a standard Normal distribution. Include an appropriately labelled sketch of the N(0, 1) curve. Complete parts (a) through (e). . . . . a. Find the area to the right of z = - 5.00. Choose the correct graph below. O A. O B. C. O D. + + + + 7 =500 7 =500 7= -500 7= -500 The area to the right of z = - 5.00 is (Round to three decimal places as needed.)