8. The Committee on Student Life did a survey of 417 students regarding satisfac

Question

8. The Committee on Student Life did a survey of 417 students regarding satisfaction with student govemment and class standing. The results are shown in the table below ROW TOTAL Not satisfied (NS) Neutral (Ne) Satisfied (S) COLUMN TOTAL 17 61 23 101 Soph) 19 35 49 103 (Sen) 12 38 65 115 23 166 180 417 GRAND TOTAL 32 98 Assume that the sample represents the entire population of customers. Find the probability that a student is: a. P(S) b. P(Sen) c. P(S | Sen) d. P(S and Sen) e. P(S or Sen) g. PINS and J) h. P(Ne or Soph)

Explanation / Answer

a)
P(S) = 180/417 = 0.4317

b)
P(Sen) = 115/417 = 0.2758

c)
P(S|Sen) = P(S and Sen)/P(Sen)
= 65/115 = 0.5652

d)
P(S and Sen) = 65/417 = 0.1559

e)
P(S or Sen)
= P(S) + P(Sen) - P(S and Sen)
= (180 + 115 - 65)/417
= 0.5516

f)
P(Ne|F)
= P(Ne and F)/P(F)
= 61/101 = 0.6040

g)
P(NS and J) = 23/417 = 0.0552

h)
P(Ne or Soph)
= P(Ne) + P(Soph) - P(Ne and Soph)
= (166 + 103 - 35)/417
= 0.5612

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