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QUESTION

# How do you find the z-score for sample mean M = 90 for a sample of n = 4?

z=(bar x-mu)/sigma

Population standard deviation must be known for calculating z scores. You can also replace this by sample s.d. if sample size is large enough.

So while you have given us the sample mean, what you really need is the sample standard deviation "s" (most common) or the population standard deviation " sigma" (less common).

HINT: when calculating the z-score make sure you use parentheses in the denominator. Otherwise you will get a very bad answer.

z = ((bar x-mu))/sigma

HINT: if you only have "s" you need to calculate the standard error first. s.e. = sqrt(s^2/n)

then the z-score is calculated by z=(bar x - mu)/(s.e.)