There are 43 students in an elementary statistics class. On the basis of years o
ID: 3133773 • Letter: T
Question
There are 43 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. (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 ofthe 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.Explanation / Answer
a)
From 6:50 to 11:00 is 250 minutes.
Hence, the mean should be less than 250/43 = 5.813953488.
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 5.813953488
u = mean = 5
n = sample size = 43
s = standard deviation = 4
Thus,
z = (x - u) * sqrt(n) / s = 1.33
Thus, using a table/technology, the left tailed area of this is
P(z < 1.33 ) = 0.9082 [ANSWER]
*****************************
b)
From 6:50 to 11:10 is 260 minutes.
Hence, the mean should be less than 260/43 = 6.046511628
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 6.046511628
u = mean = 5
n = sample size = 43
s = standard deviation = 4
Thus,
z = (x - u) * sqrt(n) / s = 1.72
Thus, using a table/technology, the right tailed area of this is
P(z > 1.72 ) = 0.0427 [ANSWER]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.