23. The time required to complete a final examination in a particular college co

Question

23. The time required to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. a. What is the probability of completing the exam in an hour or less? b. what is the probability that a student will complete in more than 60 minutes but less than 75 minutes? c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

Explanation / Answer

a) Since the standard deviation is 10 minutes, that means 60 minutes is 2 standard deviations less than the mean. According to a standard devation table, less than 2 standard deviations below the mean would only have a likelihood of 2.28%.

b) The probability of completing the exam between 60 and 75 minutes falls from 2 standard deviations less than the mean to half a deviation less than the mean. Since we said in part a that only 2.28 % was below that line , we need to look now at half a standard deviation below the mean. The chart says 30.85% of results would be expected to fall below half a standard deviation below the mean, so the amount between 60 and 75 minutes would be 30.85 - 2.28 = 28.57%.

c) 90 minutes is 10 minutes more than the mean, which is 1 standard deviation higher than the mean. One deviation higher than the mean includes 84.13% below than level, so only 15.87% would still be worknig after 90 minutes. That would work out to about 10 people would be sad when time is called.

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