# Question please use this z table below when answering  The distribution of course grades in a very large class is (approximately) Normal with mean 49 and standard deviation 13. The minimum possible grade is 0 and the maximum possible grade is 120. A grade of 60 or more is required to pass the course. The course instructor is considering the possibility of a "bell curve" that will increase the mean grade to 74 and decrease the standard deviation to 8 . Suppose the instructor will toss a fair or balanced coin to decide what to do and will use the bell curve only if the coin comes up heads. What is the probabiity that the student at the 50 -th percentile will pass the course? $$\mathbf{Z}$$ table: $$\mathbf{P ( Z s z )}$$ (You do not have to interpolate.)

TBUG8Z The Asker · Probability and Statistics
Transcribed Image Text: The distribution of course grades in a very large class is (approximately) Normal with mean 49 and standard deviation 13. The minimum possible grade is 0 and the maximum possible grade is 120. A grade of 60 or more is required to pass the course. The course instructor is considering the possibility of a "bell curve" that will increase the mean grade to 74 and decrease the standard deviation to 8 . Suppose the instructor will toss a fair or balanced coin to decide what to do and will use the bell curve only if the coin comes up heads. What is the probabiity that the student at the 50 -th percentile will pass the course? $$\mathbf{Z}$$ table: $$\mathbf{P ( Z s z )}$$ (You do not have to interpolate.)
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Transcribed Image Text: The distribution of course grades in a very large class is (approximately) Normal with mean 49 and standard deviation 13. The minimum possible grade is 0 and the maximum possible grade is 120. A grade of 60 or more is required to pass the course. The course instructor is considering the possibility of a "bell curve" that will increase the mean grade to 74 and decrease the standard deviation to 8 . Suppose the instructor will toss a fair or balanced coin to decide what to do and will use the bell curve only if the coin comes up heads. What is the probabiity that the student at the 50 -th percentile will pass the course? $$\mathbf{Z}$$ table: $$\mathbf{P ( Z s z )}$$ (You do not have to interpolate.)
&#12304;General guidance&#12305;The answer provided below has been developed in a clear step by step manner.Step1/2Let X represent the grade of a classmate chosen at random, and let Y represent the same student's grade after the instructor applies the bell curve. In the event that the instructor chooses to employ the bell curve, we want to determine the probability that Y is at least 60.Let H be the case when the instructor uses the bell curve and the coin comes up heads, and let T be the case when the instructor does not use the bell curve and the coin comes up tails. Then there are:$$\mathrm{{P}{\left({H}\right)}={P}{\left({T}\right)}=\frac{{1}}{{2}}}$$ (since the coin is fair)Explanation:Y has a normal distribution with a mean of 74 and a standard deviation of 8 if H occurs. We can write: Y and X share the same distribution if T occurs.$$\mathrm{{P}{\left({Y}≥{60}{\mid}{H}\right)}={P}{\left({Z}≥\frac{{{60}-{74}}}{{8}}\right)}}$$where the usual Normal random variable is Z.We discover: Using a typical Normal table:\( \mathrm{{P}{\left({Z}≥-{1.75}\right)}≈{0.9599 ... See the full answer