Question

the scores on a test are normally distributed with a mean of 140 and a standard deviation of 28. what is the score that is 1.5 standard deviations above the mean? the score is

Explanation:

Step1: Use the formula for a value in a normal distribution

The formula is \(x=\mu + z\sigma\), where \(\mu\) is the mean, \(z\) is the number of standard deviations from the mean, and \(\sigma\) is the standard deviation.
Given \(\mu = 140\), \(z = 1.5\), and \(\sigma=28\).

Step2: Substitute the values into the formula

Substitute the values: \(x = 140+1.5\times28\).
First, calculate \(1.5\times28 = 42\).
Then, \(x=140 + 42\).

Step3: Calculate the final value

\(x=182\).

Answer:

\(182\)