Question

the scores on a test are normally distributed with a mean of 60 and a standard deviation of 12. what is the score that is $2\frac{1}{2}$ standard deviations above the mean
a score of $\square$ is $2\frac{1}{2}$ standard deviations above the mean.

Explanation:

Step1: Convert the mixed number to an improper fraction

$2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$

Step2: Calculate the value of the score

The formula for a value \(x\) in a normal distribution is \(x=\mu+z\sigma\), where \(\mu\) is the mean, \(z\) is the number of standard deviations, and \(\sigma\) is the standard deviation.
Here, \(\mu = 60\), \(z=\frac{5}{2}\), and \(\sigma=12\)

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Answer:

\(90\)