There are 42 students in an elementary statistics class. On the basis of years o

Question

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?

Explanation / Answer

here for 42 students expected time =42*5=210 minutes

and std deviation =4*(42)1/2 =25.923

a)as three are 250 minutes b/w 6:50 PM and 11:00 PM<

hence P(X<250)=P(Z<(250-210)/25.923)=P(Z<1.543)=0.9386

b) P(X>260)=1-P(X<260)=1-P(Z<(260-210)/25.923)=1-P(Z<1.9288)=1-0.9731=0.0269

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