The time needed to complete a final examination in a particular college course i
ID: 2925401 • Letter: T
Question
The time needed to complete a final examination in a particular college course is normally distrubuted with a mean of 80 mintues and a standard deviation of 10 minutes. Answer the following questions.
a. What is the probability of completing the test in one hour or less?
b. What is the probability that a student will complet the test in more than 60 minutes but less than 75 minutes?
c. Assume that the class has 60 students and that the test period is 90 minutes in length. How many student do you expect will be unable to complete the test in the alloted time?
Explanation / Answer
Solution:
a) P (z < 60)
= P (z < 60-80/10)
= P (z <-2)
= 0.0228 or 2.28%
b) P (60 < z < 75)
= P (60 - 80/10 < z< 75-80/10)
= P (-1.67 < z < -0.42)
= 0.3375 - 0.0475
= 0.2897 or 28.97%
c) P (z > 90)
= P (z > 90-80/10)
= P (z > 0.83)
= 1 - P (z < 0.83)
= 1 - 0.7967
= 0.2033 or 20.33%
= 60 * 0.2033
= ~ 12.198 students
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