Question

In a distribution, a score of X=60 has a z-score of -3.0. A score of X=85 has a z-score of +2.0. What are the mean and the standard distribution for this population?

a. u=50, standard deviation = 10
b u=75, standard deviation = 5
c u=70, standard deviation = 2
d u=68, standard deviation = 4

Answer 1

Using the given z-scores for X=60 (-3.0) and X=85 (+2.0), we can calculate the mean (μ) and standard deviation (σ) of the population. After solving, the mean is found to be 75 and the standard deviation 5, making option b the correct answer.

Step-by-step explanation:

The given distribution specifies a score of X=60 with a z-score of -3.0, and another score of X=85 with a z-score of +2.0. From these values, we can solve for the mean (μ) and standard deviation (σ) of the population.

Given the formula for calculating a z-score:

z = (X - μ) / σ

For X=60 with z-score -3.0:

-3 = (60 - μ) / σ

We can solve for μ and σ using this equation and the one for X=85 with z-score 2.0:

2 = (85 - μ) / σ

After solving the system of equations, we find that μ = 75 and σ = 5.

The correct answer to the student's question is therefore option b: μ=75, standard deviation = 5.