In a normal distribution with mu = 100 and sigma = 4 what number corresponds to z = -3? Please explain your solution thoroughly.
To find the probability of occurrence of a number x, the number has to be standardized to a Z-score.
Z=(x-mu) / sigma
mu is the population mean
sigma is the population standard deviation
mu=100, sigma=4, Z=-3, and you need to find x.
-3 = (x-100) / 4
x-100 = -12
x= 88 is the number that correspond to a z-score = -3
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