1.3 solutions

1.3 solutions - Stat 133 Recitation SOLUTIONS Section 1.3...

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Stat 133 Recitation SOLUTIONS Section 1.3 Section 1.3: Normal Distribution 1. Suppose Math exam scores have a normal dist with mean 70 and s = 10 and stat exam scores have a normal dist with mean 80 and SD 5. a. Draw a picture of the distribution of math scores. Draw a picture of the distribution of stat exam scores. b. Bob scores 85 on the math exam. What is Bob’s Z-score? Find and interpret (explain to Bob what it means.) Z = X - Ε Ξ ( 29 Σ∆ = 85 - 70 10 = 15 10 = 1.5 He scored 1.5 standard deviation above the mean. Or he scored higher than the most of the others. c. Bob scored 85 on the math exam. What percentage of the students scored lower than Bob? Z = 1.5 from above. P(X<85) = P(Z<1.5) = .9332. d. Bob’s math exam score is at the 93.32 th percentile. (Using part c.) e. Frank is told that his z-score on the math exam was -1. What does that mean? Frank’s score is one standard deviation below the mean of the math scores. That means Frank’s score is 70-1(10)= 70-10=60 f. What percentage of the stat students scored more than 90 on the test? P(Y>90)=P Z Ξ - Ε Ξ ( 29 Σ∆ ÷ =P Z 90 - 80 5 ÷ = P(Z>2) = 1-.9772=.0228 g. What score marks the upper 10 percent of stat exam scores?
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1.3 solutions - Stat 133 Recitation SOLUTIONS Section 1.3...

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