What is the z-score of x = 12, if it is two standard deviations to the right of

Question

What is the z-score of x = 12, if it is two standard deviations to the right of the mean? What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean? What is the z-score of x = -2, if it is 2.78 standard deviations to the right of the mean? What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean? Suppose X ~ N(2, 6). What value of x has a z-score of three? Suppose X ~ N(8, 1). What value of x has a z-score of -2.25? Suppose X ~ N(9, 5). What value of x has a z-score of -0.5? Suppose X ~ N(2, 3). What value of x has a z-score of -0.67? Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean? Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the mean? Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the mean? Suppose X ~ N(-1, 2). What is the z-score of x = 2? Suppose X - N(12, 6). What is the z-score of x = 2? Suppose X ~ N(9, 3). What is the z-score of x = 9?

Explanation / Answer

Answers

12. z-score = -1.5

Hint: z-score indicates how many standard deviations an element is from the mean

14. z-score = -0.133

16. Given that X ~ N (8, 1), Z = -2.25

Z = (X – )/

Therefore, X = + Z = 8 + (-2.25 * 1) = 5.75

18.

Given that X ~ N (2, 3), Z = -0.67

Therefore, X = + Z = 2 + (-0.67 * 3) = -0.01

20.

Given that X ~ N (4, 2), Z = 2

Therefore, X = + Z = 4 + (2 * 2) = 8

22. Given that X ~ N (-1, 2), X = 2

Z = (X – )/ = (2 + 1)/2 = 1.5

24. Given that X ~ N (9, 3), X = 9

Z = (X – )/ = (9 - 9)/3 = 0

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