There are 48 students in an elementary statistics class On t

There are 48 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.

Solution

The time needed to graph paper, x ~N(5,4)
The total time needed to grade all 48 papers, T = X ~ N(48*5, Sqrt(48 * 4)
That is T ~ N(240,27.7128) => Mean = 240, s.d = 27.7128

a)
if gradeing timesa are independent and the instructor begins grading
at 6:50 PM and grades are continuously then the probability that he
is through grading before the 11:00 PM t.v begins,
that is , he will completely grade all 46 papers in 10+4*60 = 250 mins
P(X < 250) = (250-240)/27.7128
= 10/27.7128= 0.3608
= P ( Z <0.3608) From Standard Normal Table
= 0.6409 ~ 64.09% of chance to grade all papers before 11.00 PM
b)
he will take more than 10+4*60+10=260 min to grade all 46 papers
P(X > 260) = (260-240)/27.7128
= 20/27.7128 = 0.7217
= P ( Z >0.722) From Standard Normal Table
= 0.2352                  
23.52% of chance to miss the part of the news that starts from 11:10 PM