In a Statistics course the professor uses the following grading policy: the bottom 5% of students receive an F, the next 10% receive a D, the next 40% receive a C, the next 30% receive a B, and the rest receive an A. Assume Students grades are Normally distributed with a mean of 70 and standard deviation of 10 b. Draw the distribution with the Cut-off scores for each letter grade (A/B, B/C, C/D, D/F) Find the probability that a randomly selected student gets an 80 or better? i. First attempt to integrate the PDF. (Hint: Recall the Gaussian integral identity) ii. Standardize to find the probability Probability that a student scores between 60 and 75 i. First attempt to integrate the PDF. (Hint: Recall the Gaussian integral identity) ii. Standardize to find the probability

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In a Statistics course, the professor uses the following grading policy: the bottom 5% of students receive an F, the next 10% receive a D, the next 40% receive a C, the next 30% receive a B, and the rest receive an A. Assume students' grades are normally distributed with a mean of 70 and a standard deviation of 10.

a. Draw the distribution with the cut-off scores for each letter grade (A/B, B/C, C/D, D/F).

b. Find the probability that a randomly selected student gets an 80 or better?
   i. First attempt to integrate the PDF. (Hint: Recall the Gaussian integral identity).
   ii. Standardize to find the probability.

c. Probability that a student scores between 60 and 75.
   i. First attempt to integrate the PDF. (Hint: Recall the Gaussian integral identity).
   ii. Standardize to find the probability.
Transcribed Image Text:In a Statistics course, the professor uses the following grading policy: the bottom 5% of students receive an F, the next 10% receive a D, the next 40% receive a C, the next 30% receive a B, and the rest receive an A. Assume students' grades are normally distributed with a mean of 70 and a standard deviation of 10. a. Draw the distribution with the cut-off scores for each letter grade (A/B, B/C, C/D, D/F). b. Find the probability that a randomly selected student gets an 80 or better? i. First attempt to integrate the PDF. (Hint: Recall the Gaussian integral identity). ii. Standardize to find the probability. c. Probability that a student scores between 60 and 75. i. First attempt to integrate the PDF. (Hint: Recall the Gaussian integral identity). ii. Standardize to find the probability.
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