8. 14 pts] In a Statistics 207 course, the distribution of the number of points

Question

8. 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 Total (a) [3 pts| Find the expected value of the number of points (to 2 decimal places) b) 4 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

8a)

a) from above expected value =2.85

b) std deviaiton =1.35

c) expected value of average =E(Xbar) =(E(x1)+E(x2)+E(x3))/3 =(2.85+2.85+2.85)/3 =2.85

standar deviation =((1/32)*(Var(x1)+Var(x2)+Var(x3))1/2= 1.35/(3)1/2 =0.78

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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