Question

5. For the first midterm in ECON 3402, the average score is 76 and the standard deviation is 5.5. (a) Not wanting to let his students down, Trung decides to add 10 points to all scores. What would this do to the mean and the standard deviation? (b) What would a 5 percent increase in all scores do to the mean and the standard deviation?

Answer 1

Given: mean EC%) = 76 standard deviation SD (X)= 5.5 a added to points to all scores. He Y x +10. .:ECF)- ECX+10) = E(X2+10 = 76 +10 ECY) = 36 SD(Y) = 50(x+10) = SOCX SDCY) = 5.5 :mean 15 [86] and standard deviation (s[5.5 That is mean increased by 10 points , but standard is not changed deviation 5 percent increase 70 all scores - EY Z = x+ 5 percentage increase a E(ZIE E(X +39.) = E(X) + 544 76 * 5%. 5D(?= 80(X+57) 50(X) 5.5 The mean will also increases to 5x 5 percent but, standard deviation will not change