6. A Biology professor was curious about the distribution of performance among u

Question

6. A Biology professor was curious about the distribution of performance among upper and lower classmen in his introductory biology course. Below is the distribution of students based on their class standing (Lower classman = Freshman or Sophomore: Upper Classman = Junior or Senior) and their performance in the course (Passed = C or higher; Failed = D or F; withdrew withdrew from class prior to final grade). Upper Classmen 65 Lower Class Total Passed Failed Withdrew Total 305 100 15 150 20 250 men 105 30 60 170 (a) If a student is randomly selected what is the probability that the student is a Lower Classman or Withdrew from the course? (b) Are students more likely to fail if they are Upper Classmen or Lower Classmen? Explain.

Explanation / Answer

Ans:

To get joint probability distribution,divide the each entry of above table by 250.

a)P(lower classman or withdrew )=P(lower classman)+P(withdrew)-P(lower classman and withdrew)

=0.6+0.08-0.06

=0.62

b)

P(fail/upper classmen)=P(fail and upper classmen)/P(upper classmen)=0.12/0.4=0.3

P(fail/lower classmen)=P(fail and lower classmen)/P(lower classmen)=0.12/0.6=0.2

Probability of failing given that they are from upper classmen is 0.3,which is higher than the probabilty

of failing given that they are from lower classmen is 0.2.

Hence,students are more likely to fail if they are from upper classmen.

Passed Failed Withdrew Total Upper Classmen 65 30 5 100 Lower Classmen 105 30 15 150 Total 170 60 20 250 Joint probability distribution Passed Failed Withdrew marginal prob. Upper Classmen 0.26 0.12 0.02 0.4 Lower Classmen 0.42 0.12 0.06 0.6 Marginal prob. 0.68 0.24 0.08 1

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