The time for a professor to grade a homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that randomly selected homework will require more than 12 minutes to grade?

Accepted Solution

Answer:59.48%Step-by-step explanation:To determine the probability you have to calculate the z score which is equivalent to the number of standard deviations you are from the mean.[tex]z = \frac{x-\mu}{\sigma}[/tex]x is the value you want to know its probabilityμ is the meanσ is the standard deviation[tex]z = \frac{12-12.6}{2.5} =-0.24[/tex]A z score of -0.24 means you are 0.24 standard deviation at the left of the mean, the probability associated to a z of -0.24 can be found in a z table and it is 40.52%.That probability cover the minimum value until 12 minutes, so the probability to need more than 12 minutes is 100 - 40.52 = 59.48%