O-CAplia- Student Registration Ins Cengage Aple Student antion x Graded Assignme

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O-CAplia- Student Registration Ins Cengage Aple Student antion x Graded Assignment | Back to Assignment Due Sunday 02.18.18 at 11:45 PM Attempts: Score: /2 4. Chapter 4, Problem 7 Aa on an exam with a mean of = 75, you obtain a score of X-80. would you prefer a standard deviation of -2 or o-10? (Hint. T visuake each possbility in the accompanying Normal Distribution tool, set the mean to -75, set the standard deviation too-2, and drag the orange vertea ine on the graph to x 80; then change the standard devilation to a 10 and put the orange line back to x 80.) Normal Distributios Mean a 75 Standard Deviation-7 Prefer“ 10 Prefer -2 your score was X-70, would you prefere-20r -10°Hinti Again, you can use the Normal Ostribution too to visualize how the value of o affects your position relative to the rest of the class when x 70.) O Prefer o 10 Prefer o-2

Explanation / Answer

z-score = (X - mean)/sd
= (80 - 75)/sd
= 5/sd

higher the z-score, better is the performance
hence
sd = 2 is better in case X = 80

for X = 70
z = (70 -75)/sd
= -5/sd

now note that z-score is negative
hence sd = 10 will make it larger
as z = -5/10 = -0.5
for sd = 2
z = -2.5
hence -0.5 > -2.5
sd = 10 is better if X = 70

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