14 pts In a Statistics 207 course, the distribution of the number of points on a

Question

14 pts In a Statistics 207 course, the distribution of the number of points on a short answer exam question is shown in the table below. No. of points Percent scores 15 15 30 25 10 100 4 Total (a) |3 ptsl Find the expected value of the number of points (to 2 decimal places). (b) 14 pts] Find the standard deviation of the number of points (to 2 decimal places). (c) 7 pts] Suppose you have a sample of 3 independently and randomly chosen students (assume with replacement). Find the expected value and standard deviation of the average number of points in these three students.

Explanation / Answer

a) expected mean =2.85

b) std deviation =1.35

c)let there score are x1,x2,x3 and average X=(x1+x2+x3)/3

expected value of average number of points E(X) =(1/3)*(E(x1)+E(x2)+E(x3)) =(1/3)*(2.85+2.85+2.85) =2.85

Variance of average points Var(X)=(1/32)*(Var(x1)+Var(x2)+Var(x3)) =(1/9)*(1.352+1.352+1.352) =1.352/3

hence std deviation of average points SD(X) =(1.352/3)1/2 =1.35/(3)1/2=0.78

points x p(x) xP(x) (x-)2 (x-)2P(x) 0 0.050 0.000 8.123 0.406 1 0.150 0.150 3.423 0.513 2 0.150 0.300 0.722 0.108 3 0.300 0.900 0.023 0.007 4 0.250 1.000 1.323 0.331 5 0.100 0.500 4.623 0.462 total 1 = 2.850 18.235 2= 1.8275 std deviation=     =    2 = 1.3519

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