Question

A certain test is designed to measure the satisfaction of an individual with his/her relationship. Suppose that the scores on this test are approximately aormaliy distributed with a mean of 50 and a standard deviation of 9 . An individual with a score of 35 or less is considered dissatisfied with his/mer refationship. According to this criterion, what proportion of people in relationships are dissatisfied?

Answer 1

Approximately 4.75% of people in relationships are considered dissatisfied based on the test score criteria, which is determined by calculating the z-score for 35 and finding the corresponding percentile from the standard normal distribution.

Step-by-step explanation:

To determine what proportion of people in relationships are considered dissatisfied based on a score of 35 or less on a test with a normal distribution, we need to calculate the z-score for 35 and then use the standard normal distribution to find the corresponding percentile.

The z-score is calculated using the formula:

Z = (
X −
μ) /
σ

Where X is the score,
μ is the mean, and
σ is the standard deviation. Plugging in the values for this scenario, we get:

Z = (35 − 50) / 9 = − 1.67

Next, we use a standard normal distribution table or a calculator to find the percentile corresponding to a z-score of − 1.67, which will tell us the proportion of individuals who score 35 or less. The percentile for z = − 1.67 is approximately 0.0475.

So, approximately 4.75% of people in relationships are considered dissatisfied according to this test. This means that if 100 people took this test, approximately 5 would be classified as dissatisfied.