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: Calculate the value of 1.5 standard deviations

The standard deviation is \( \sigma = 28 \). The value of 1.5 standard deviations is \( 1.5\times\sigma\).

$$1.5\times28 = 42$$

Step2: Find the score that is 1.5 standard deviations above the mean

The mean is \( \mu=140 \). The score \( x\) that is \( k = 1.5\) standard deviations above the mean is given by the formula \( x=\mu + k\sigma\).

$$x=140+42$$

$$x = 182$$

Answer:

182