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Self Assessment for Lesson 12 1. Click on “Begin Assessment” button. 2. Scroll down to begin quiz. 1 Self Assessment for Lesson 12 2 1. Which one of the following is a false statement about a standardized value (z-score)? It represents how many standard devations an observation lies from the mean. It represents in which direction an observation lies from the mean. It is measured in the same units as the variable. 2. Rachael got a 670 on the analytical portion of the Graduate Record Exam (GRE). If GRE scores are normally distributed and have mean µ = 600 and standard deviation σ = 30, what is her standardized score? Self Assessment for Lesson 12 3 3. The length of human pregnancies from conception to birth is known to be normally distributed with a mean of 266 days and standard deviation of 16 days. What proportion of pregnancies last between 250 and 274 days? 4. In a certain marathon, the average time to complete the race was normally distributed with mean µ = 4.15 hours and standard deviation σ = 0.84 hours. If we wanted to give medals to the 4% of the runners with the best times, what would be the slowest time that would receive a medal? Self Assessment for Lesson 12 4 5. Suppose the lengths of sport-utility vehicles (SUV) are normally distributed with mean µ = 190 inches and standard deviation σ = 5 inches. Marshall just bought a brand-new SUV that is 194.5 inches long and he is interested in knowing what percentage of SUVs are longer than his. Using his statistical knowledge, he drew a normal curve and labeled the appropriate area of interest. Which picture best represents what Marshall drew? Plot B 0.4 0.4 Plot A 0.3 Area of Interest 0.0 0.0 0.1 0.1 0.2 0.2 0.3 Area of Interest -4 -2 0 2 Standard Normal Curve Plot A 4 -4 -2 0 2 Standard Normal Curve Plot B 4 Self Assessment for Lesson 12 5 Click on the button below to see how you did. Questions correct: Percentage correct: Click on the “Correct” button to highlight your correct answers in green and wrong answers in red. For question solutions either: • shift-click on the “Ans” button that appears next to the free-response box or • shift-click on the correct answer for the multiple choice questions. Solutions to Quizzes 6 Solutions to Quizzes Solution to Quiz: units of measure. 1. The z-score does not have any End Quiz Solutions to Quizzes 7 Solution to Quiz: 2. To find standardized scores, you use the following formula: z= x−µ σ In this case, it is found by z= 670 − 600 = 2.33 30 End Quiz Solutions to Quizzes 8 Solution to Quiz: 3. First, draw the picture. Then find the z-scores for both 250 and 274. The z-score for 250 is found by 250−266 = −1. Similarly, the z-score for 274 is 16 274−266 = 0.50. Now go to the standard normal table and 16 see that the area to the left of 0.50 is 0.6915. The area to the left of −1 is 0.1587. Subtracting off the smaller area gives the final answer of 0.6915 − 0.1587 = 0.5328. End Quiz Solutions to Quizzes 9 Solution to Quiz: 4. First, draw the picture. Because in racing, the smallest times are the best times, we want that 4% to be on the left side of the mean. So we go to the table and find the z-score that has area that is closest to 4%, or 0.0400. That z-score is −1.75. We can now use our formula to solve for that time. So z= x − 4.15 = −1.75 0.84 and by solving this for x we find that the time you would have to have would be 2.68 hours. End Quiz Solutions to Quizzes 10 Solution to Quiz: 5. Because we are looking for the probability of being greater than z = 0.90, we need to choose the area on the right. That area is correctly identified in Plot B. End Quiz