Respuesta :
Answer:
The z-score (value of z) for this sample mean is 1.
Step-by-step explanation:
We are given that a random sample of n = 4 scores is selected from a population with a mean of 50 and a standard deviation of 12.
Also, the sample mean is 56.
The z-score probability distribution for a sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 50
[tex]\sigma[/tex] = standard deviation = 12
[tex]\bar X[/tex] = sample mean = 56
n = sample size = 4
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, we are given that the sample mean is 56 for which we have to find the z-score (value of z);
So, z-score is given by = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] = [tex]\frac{56 - 50}{\frac{12}{\sqrt{4} } }[/tex] = 1
Hence, the z-score (value of z) for this sample mean is 1.
