5. Suppose you are interested in the labor force participation among UIC student

Question

5. Suppose you are interested in the labor force participation among UIC students and decide to randomly survey 10 students on campus. You want to ask students whether they work at least part-time, and the answer is either Yes" or "No". Denote the question as variable X, and X-1 if the student answers "Yes". Previous studies indicate that the probability of a college student working at least part-time is 0.4. We also assume that a student's choice of labor force participation is independent of each other. (a) What type of distribution does X have? 3 of 4 EC270 Homework #2 Due Feb 27 (b) What is the expected value of X? (c) What is the standard deviation of X? (d) Suppose you're interested in the probability of observing 4 students working at least half- time out of 10 interviews. Calculate the probability. Please show the work

Explanation / Answer

Ans:

a)X has binomial distribution with n=10,p=0.4

b)Expected value=np=10*0.4=4

c)standard deviation=sqrt(np(1-p))=sqrt(10*0.4*0.6)=1.55

d)P(x=k)=10Ck*0.4k*(1-0.4)10-k

P(x=4)=10C4*0.44*0.66=0.2508

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