The faculty at Garland High School consists of 70% women. If an 8-person committee is selected at random to oversee homecoming festivities, what is the expected number of wmen on this commitee?
A. 80(0.70)
B. 8(0.30)
c.square root 8(.70)(.030)
d. 8(.70)(.30)
A. 80(0.70)
B. 8(0.30)
c.square root 8(.70)(.030)
d. 8(.70)(.30)
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I am assuming that every faculty member has the same probability of being chosen for each position. The expectation of the sum is equal to the sum of the expectations.
Let X be the number of women filling one position.
Let Y be the number of women on the committee.
E[X] = 0.7
E[Y] = E[8X] = 8E[X] = 8(0.7) = 5.6
Let X be the number of women filling one position.
Let Y be the number of women on the committee.
E[X] = 0.7
E[Y] = E[8X] = 8E[X] = 8(0.7) = 5.6