2. +-/2 points DevoreStat95·E.049 My Notes + Ask Your Teacher There are 42 stude
ID: 3321993 • Letter: 2
Question
2. +-/2 points DevoreStat95·E.049 My Notes + Ask Your Teacher There are 42 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.) (a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins? (b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV? You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Talk to a TutorExplanation / Answer
Solution:
The mean and standard deviation of time needed to grade students are 6 and 4 minutes respectively. There are 40 students. That is n = 42, = 5, = 4.
Then,
T = n = 5(42) = 210 min
T = n = 4(42) = 25.9 min
a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, the(approximate) probability that he is through grading before the 11:00 P.M TV news begins is,
P(T < 250) = P(T- T/T < 250 - 210/25.9)
= P(z < 1.5444)
= 0.9382
b) If the sports report begins at 11:10, the probability that he misses part of the report if he waits until grading is done before turning on the TV is,
P(T > 260) = P(T- T/T > 260 - 210/25.9)
= P(z > 1.9305)
= 1P(Z < 1.9305 )
= 10.9732 = 0.0268
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