Question

The verbal portion of the gre has a mean = 500 and a standard deviation = 100. a random sample of 25 students (n = 25) obtained an average gre score of m = 505. what is the z score for the m = 505 on the distribution of sample means?

Answer 1

The z-score for an average GRE score of m = 505 on the distribution of sample means is 0.25, indicating that the sample mean is 0.25 standard deviations above the population mean.

Step-by-step explanation:

To calculate the z-score for the average GRE score of m = 505 on the distribution of sample means, we would use the formula:

z = (X - μ)/(σ/sqrt(n))

Where:

• X is the sample mean (505)
• μ is the population mean (500)
• σ is the population standard deviation (100)
• n is the sample size (25)

Substitute the values into the formula:

z = (505 - 500)/(100/sqrt(25))

z = (505 - 500)/(100/5)

z = (5)/(20)

z = 0.25

The z-score of 0.25 means that the sample mean of 505 is 0.25 standard deviations above the population mean of 500. This indicates the position of the sample mean relative to the population mean in a standard normal distribution.