A sample from a population with μ = 40 and σ = 10 has a mean of M = 44.If the sample mean corresponds to a z = 2.00,then how many scores are in the sample?
A)n = 100
B)n = 25
C)n = 5
D)n = 4

Question

A sample from a population with μ = 40 and σ = 10 has a mean of M = 44.If the sample mean corresponds to a z = 2.00,then how many scores are in the sample?​
A)​n = 100
B)​n = 25
C)​n = 5
D)​n = 4

Quizplus · Accepted Answer

The formula to calculate the z-score is $z = \frac{M - \mu}{\sigma / \sqrt{n}}$, where $M$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Rearranging the formula to solve for $n$, we get $n = \left(\frac{\sigma \cdot z}{M - \mu}\right)^2$. Plugging in the given values ($\sigma = 10$, $z = 2.00$, $M = 44$, $\mu = 40$), we find $n = \left(\frac{10 \cdot 2}{44 - 40}\right)^2 = 25$.

A Sample from a Population with μ = 40 and σ