Question

the mean score on a particular test is 79 and the standard deviation is 5.5. what is the probability that a randomly selected test score is more than 90? use the empirical rule to solve. (1 point)
34%
68%
2.5%
16%

Explanation:

Step1: Calculate the number of standard deviations from the mean

The formula for the number of standard deviations \(z=\frac{x - \mu}{\sigma}\), where \(x = 90\), \(\mu=79\), \(\sigma = 5.5\).

$$z=\frac{90 - 79}{5.5}=\frac{11}{5.5}=2$$

Step2: Apply the Empirical Rule

The Empirical Rule states that for a normal distribution:

• Approximately \(95\%\) of the data lies within \(z=- 2\) and \(z = 2\).
• The remaining data is \(100\%-95\% = 5\%\).
• This remaining \(5\%\) is split evenly between the two tails. So the percentage of data in the right - tail (\(z>2\)) is \(\frac{5\%}{2}=2.5\%\)

Answer:

\(2.5\%\)