Test Score Deviation

Solution

Answer: 5

We are given \[ P(X < 65) = 0.84. \] We can find \[ Z = \frac{X-\mu}{\sigma}. \] Thus \[ P\!\left(Z < \frac{65-60}{\sigma}\right) = 0.84. \] From the empirical rule for the normal distribution, about \(84\%\) of the distribution lies below one standard deviation above the mean. Therefore \[ P(Z < 1) \approx 0.84. \] Thus \[ \frac{65-60}{\sigma} = 1. \] \[ \sigma = 5. \] So the standard deviation is 5.