Suppose X ~ N(2, 3). What value of x has a z-score of -0.67?
If the area to the left of x in a normal distribution is 0.161, what is the area to the right of X?
ANSWER :
54
x = N(µ, var.) = N(2, 3)
=> µ = 2 and var. = 3
=> s = SD = sqrt(var) = sqrt(3) = 1.732
z score = (x - µ)/s = (x - 2)/1.732
=> - 0.67 = (x -2)/1.732
=> x = -0.67*1.732 + 2 = 0.8396 (ANSWER).
55
Area to the right
= 1 - area to the left
= 1 - 0.161
= 0.839 (ANSWER)
Suppose X ~ N(2, 3). What value of x has a z-score of three?
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