Question

a score that is 3 points lower than the sample mean has a z-score of z = -0.25, and a score of x = 44 has a z-score of –0.75. what is the sample mean?

Answer 1

To find the sample mean, use the formula for the z-score and set up two equations to solve for the mean.

Step-by-step explanation:

To find the sample mean, we can use the formula for the z-score:

z = (x - μ) / σ

where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.

From the information given, we have:

z = -0.25 when x = sample mean - 3

z = -0.75 when x = 44

Plugging in these values, we can set up two equations to solve for the sample mean:

Equation 1: -0.25 = (sample mean - 3 - μ) / σ

Equation 2: -0.75 = (44 - μ) / σ

Solving these equations simultaneously will give us the sample mean.