Question
Students in a class take a quiz with eight questions. The number x of questions answered correctly can be Complete parts (a) through (e) (a) Use the probability distribution to find the mean of the probability distribution mu = (Round to the nearest tenth as needed) (b) Use the probability distribution to find the variance of the probability distribution. sigma^2 = (Round to the nearest tenth as needed) (c) Use the probability distribution to find the standard deviation of the probability distribution (Round to the nearest tenth as needed) (d) Use the probability distribution to find the expected value of the probability distribution. (Round to the nearest tenth as needed) (e) Interpret the results. A. The expected number of questions answered correctly is 1.9 with a standard deviation of 5.1 question. B. The expected number of questions answered correctly is 5.1 with a standard deviation of 0.04 question. C. The expected number of questions answered correctly is
Explanation / Answer
a) Mean = 0*0.04+1*0.01+2*0.06+3*0.08+4*0.11+5*0.23+6*0.25+7*0.15+8*0.07 = 5.1 (nearest tenth)
b) Variance = 0*0*0.04+1*1*0.01+......8*8*0.07-(Mean^2) = 3.6 (nearest tenth)
c) Standard deviaton = Sqrt(Variance) = 1.9 (nearest tenth)
d) Expectation will be same as the mean = 5.1 (nearest tenth)
e) Option C is Correct