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

where:

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= -12+100

x= 88 is the number that correspond to a z-score = -3

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