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There are 45 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? .8243 0.8243 (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? .0961 0.0961

Respuesta :

Answer:

Step-by-step explanation:

Let X be the random variable for the time needed to grade a randomly chosen first examination paper

X is N(5, 4)

a)

Time taken=11.00-6.50=4hours 10 min=25/6 hours

P(X<25/6) =P(Z<[tex]\frac{\frac{25}{6}-5 }{4} =P(Z<-0.21)[/tex]

=0.5-0.0832=0.0168

b) Time >11.10-6.50 = 4 hours 20 mint = 13/3 hours

P(X>13/3) = P(Z>-0.16) = 0.5636

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