A random sample of n = 9 scores is obtained from a population with μ = 50 and σ = 9. If the sample mean is M = 59, what is the z-score corresponding to the sample mean?
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To find the z-score corresponding to a sample mean, we can use the formula:
z = (M - μ) / (σ / sqrt(n))
where M is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, the sample mean M is 59, the population mean μ is 50, the population standard deviation σ is 9, and the sample size n is 9.
Plugging these values into the formula, we get:
z = (59 - 50) / (9 / sqrt(9))
Simplifying:
z = 9 / (9 / 3)
z = 3
Therefore, the z-score corresponding to the sample mean of 59 is 3.