There are 42 students in answers to four decimal places) an elementary statistic
ID: 3056034 • Letter: T
Question
There are 42 students in answers to four decimal places) an elementary statistics ass. On the basis of years of experience, the instructor knows that the time needed to grace s randomly chosen first examination poper is a random variable ith an expected value of 5 min and a standard deviation of 4 min. (Round your (a) If grading times are independent and the instructor begins grading at 6:50 PM. and grades continuousty, what is the (approximate) Drobabil ty that he s through gradng before the 110 PM. TV news begins? (b) If the sports report begins at 11:10, what is the probability that he misses part of the report he waits until grading is done before turning on the TV?Explanation / Answer
Solution:
The mean and standard deviation of time needed to grade students are 5 and 4 minutes respectively. There are 42 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 - 240 /25.9)
= P(z < 0.3861)
= 0.6517
(b) If the sports reportbegins 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 - 240 /25.9)
= P(z > 0.7722)
= 1P(Z < 0.7722)
=10.7794
= 0.2206
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