Standard deviations + P-value

Question

For a normal distribution, find the probability that a measurement is: (a) more than two standard deviations above the mean (b) more than two standard deviations below the mean (c) more than 1.67 standard deviations above the mean (d) more than 0.85 standard deviations below the mean (e) less than 1.33 standard deviations below the mean

Answer 1

These problems can all be addressed using the Normalcdf function.

a. P(Z>2) = Normalcdf(2,1000,0,1) = 0.0228

b. P(Z<-2) = Normalcdf(-1,000, -2,0,1) =0.0228

c. P(Z>1.67) = Normalcdf(1,67, 1000, 0, 1) = 0.047

d. P(Z<-0.85) = Normalcdf(-1,000, -0.85, 0, 1) = 0.1977

e. P(Z<-1.33) = Normalcdf(-1,000, -1.33, 0, 1) = 0.0918