For a normal distribution that has a mean of 100 and a stan

Solution

For a normal distribution that has a mean of 100 and a standard deviation of 8. Determine the Z-score for each of the following X values:
X=70 Z=-3.75
X=124 Z=3
Use the information in 1 to determine the area or probability of
p(92 < x < 108) = ?
z(92) = (92-100)/8 = -1
z(108) = (108-100)/8 = 1
P(92 < x < 108) = P(-1 < z < 1) = 0.6827
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p(84 < x < 116) = ?
z(84) = (84-100)/8 = -2
z(116) = (116-100)/8 = 2
P(84 < x < 116) = P(-2 < z < 2) = 0.9545
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p(x < 84) = ?
z(84) = -2
P(x < 84) = P(z < -2) = P(-100< z < -2) = 0.0228