Question

A counselor records the number of disagreements (per session) among couples during group counseling sessions. If the number of disagreements is distributed normally as 4.4 ± 0.4 (M ± SD) disagreements, then what proportion of couples disagree at least 4 times during each counseling session?

Answer 1

This is a z-sores problem, follow the steps below:

We are given:

Mean = μ = 4.4

Standard Deviation = σ = 0.4

Random value = x = 4

Next, we need to find what is the normalized score of random member x using the formula:

z-score = $\frac{(x-\mu)}{\sigma}$

z-score = $\frac{4 - 4.4}{0.4} = \frac{-0.4}{0.4} = -1$

Next, we have the probability:

P(x > x1) = 1 - P(x < x1)

Using any standard z-score table we can find that:

P(x < x1) = 0.1587

P(x > x1) = 1 - 0.1587 = 0.8413

The proportion of couples that disagree at least 4 times during each counseling session is 0.8413.

Answer:

0.8413