Question

For a population with u=69 and standard deviation = 4, which of the following X scores will convert to a positive z-score of magnitude greater than 1.0

a.X=62
b.X=65
c.X=74
d. X=72

Answer 1

For the given population parameters, only the score X=74 will convert to a positive z-score greater than 1.0, which is 1.25.

Step-by-step explanation:

To find which score will convert to a positive z-score of magnitude greater than 1.0 for a population with a mean (μ) of 69 and a standard deviation (σ) of 4, we use the z-score formula:

z = (X - μ) / σ

Where X is the score in question. Let's calculate each option:

• X=62: z = (62 - 69) / 4 = -7 / 4 = -1.75 (Not a positive z-score)
• X=65: z = (65 - 69) / 4 = -4 / 4 = -1 (Not a positive z-score)
• X=74: z = (74 - 69) / 4 = 5 / 4 = 1.25 (A positive z-score greater than 1.0)
• X=72: z = (72 - 69) / 4 = 3 / 4 = 0.75 (A positive z-score, but not greater than 1.0)

Among the given options, X=74 converts to a positive z-score greater than 1.0.