2) A local unemployment office keeps track of the number of new claims files eac

Question

2) A local unemployment office keeps track of the number of new claims files each day. Based on the data collected, it determines that the following probability distribution applies:

a) What is the expected number of new claims filed each day?

b) What is the standard deviation in the number of new claims filed each day?

c) What is the expected number of new claims filed each week? Assume the unemployment office is open 5 days a week.

d) What is the standard deviation in the number of new claims filed each week? Assume the unemployment office is open 5 days a week.

Number of Claims Probability 0 0.05 1 0.15 2 0.25 3 0.45 4 0.10

Explanation / Answer

a)  expected number of new claims filed each day = =2.40

b) standard deviation in the number of new claims filed each day ==1.0198

c) expected number of new claims filed each week =5*2.40 =12

d) tandard deviation in the number of new claims filed each week =1.0198*(5)1/2 =2.2804

x p(x) xP(x) x2P(x) (x-)2 (x-)2P(x) 0 0.0500 0.000 0.000 5.760 0.288 1 0.1500 0.150 0.150 1.960 0.294 2 0.2500 0.500 1.000 0.160 0.040 3 0.4500 1.350 4.050 0.360 0.162 4 0.1000 0.400 1.600 2.560 0.256 total 1 = 2.40 6.800 10.800 2= 1.0400 std deviation=     =    2 = 1.0198

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