12. In 2015, American Pharoah won the Triple Crown in horse racing by winning th

Question

12. In 2015, American Pharoah won the Triple Crown in horse racing by winning three different races of three different lengths. Its time in each race is presented below along with the population mean and population standard deviation of winning times for each race. Assume all three distributions are normal and that the times are given in seconds. Kentucky Derby: Completed in 123 seconds; = 124 and = 3 B. A. 2 1.5 Preakness Stakes: Completed in 118 seconds; -116 and C. Belmont Stakes: Completed in 146 seconds; = 149 and Order American Pharoah's races from best to worst finishes relative to the previous winning times in the respective races. A, B, C b. A, C, B c. B, A, C d. B, C, A e. C, A, B (Lower times are better in a race so order the Z-scores from smallest to largest) f. C, B,A Use the following scenario for Questions 13, 14, and 15. The number of hours that college students spend at work per week varies by the number of credits they are taking, but distributions tend to be normally distributed. Fewer than 9 credits: = 15 and = 5 9 to 12 credits: = 10 and = 3 13 to 16 credits: 8 and = 2.25 17 or more credits: = 5 and = 1.10 .

Explanation / Answer

Question 12

Here we have to find Z values for each performances

(a) For Kentucky Derby :

Z = (X- )/ = (123 - 124)/3 = -0.333

(b) For Preakness Stakes

Z = (X- )/ = (118 - 116)/2 = 1

(c) For Belmont Stakes

Z = (X- )/ = (146 - 149)/1.5 = -2

Here the minimum Z is -2 and maximum Z is 1

so the best performance C, A & B [Option 4 is correct]

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