For a set of data with 5 ± 1.5,at least 95% of scores are greater than 3.0.

Question

Quizplus · Accepted Answer

If we assume that the data follows a normal distribution, we can use the formula:

z = (x - μ) / σ

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

For the given data, the mean is 5 and the standard deviation is 1.5. Let's compute the z-score for 3:

z = (3 - 5) / 1.5 = -1.33

Using a standard normal table, we find that the proportion of scores greater than z = -1.33 is 0.9082. Therefore, the proportion of scores less than or equal to 3 is:

1 - 0.9082 = 0.0918

or about 9%. This means that at least 91% of scores are greater than 3.0, so the statement "at least 95% of scores are greater than 3.0" is false.

For a Set of Data with 5 ± 1