Question

the scores on a standardized test are normally distributed with a mean of 95 and standard deviation of 25. what test score is 1.6 standard deviations below the mean?

Explanation:

Step1: Recall 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. Here, \(\mu = 95\), \(z=- 1.6\) (since it's below the mean), and \(\sigma = 25\).

Step2: Substitute the values into the formula

\(x=95+(-1.6)\times25\). First, calculate \((-1.6)\times25=-40\). Then, \(x = 95-40\).

Step3: Calculate the result

\(x=55\).

Answer:

\(55\)