Question

the scores on a test are normally distributed with a mean of 70 and a standard deviation of 14. find the score that is one and one - half standard deviations below the mean. a score of is one and one - half standard deviations below the mean.

Explanation:

Step1: Calculate the value of one - and - one - half standard deviations

The standard deviation \(\sigma = 14\). One - and - one - half standard deviations is \(1.5\sigma\).

$$1.5\times\sigma=1.5\times14 = 21$$

Step2: Find the score below the mean

The mean \(\mu = 70\). The score that is one - and - one - half standard deviations below the mean is \(\mu-1.5\sigma\).

$$70 - 21=49$$

Answer:

\(49\)