Question

4 pts Question 47 8, find the Z-score corresponding to each of the following X For a population with a h = 40 and o = values: a. X-42; b. X-52; c. X=36; d. X-32 HTML Editor

Answer 1

47. For the given population with M= 40 and Standard deviation, =8. We have to find the Z Score corresponding each x. For a population with mean le and standard deviation o Z Score = where x is x-4 the each value in the data set. (a)x= 42 X-4 42-40 Z score 0.25 8 8 Therefore Z score = 0.25 (6) X= 52 Z score = X-H 52-40 8 12 8 =105 Thus, z score = 1.5 (c) X=36 x-le -0.5 Z Score 36-40 8 Therefore, a score = -0.5 (d) x = 32 z score *-. 32-40 32-40 8 Therefore a score = -1

48. Given what the original population has mean, le= 43 and Standard deviation, r = 8. And we have to create a new population distribution with l=50 and On 10. Let Xo be the Original x value and het XN be the new x value. First we will find the Z score corresponding to each value of x in the original distributi- on Z score, Z= X-43 8 Then we will change this z score into new x Value (x) which has mean, l=50 and XN = 4+ Zo - 50+(z x 10) -10 x = 43 ist we find the score = 43-43 メー上 8 80 If z=0 then XN = 4+ZO- 50 +10) Thus, the new X Value 50

(6) X = 47 Z score z = 47-43 0.5 8 Z=0.5 → XN = Hn + ZON = 50+ (0.5x10) = 5075 - 55 The new x value 55 (C) X=55 z score, z=55-43 X-H 8 = 12 1.5 믕 Z = 15 → XN = Hn ZON = 50 + (1.5 x 10)=50+15 65 Thus the new value of x = 65 (d) X = 35 Z Score ) z = 35-43 8 -8 Z=-1XN = MN+ ZON= 50+ (-1x10) = 50-10 = 40 Thus the new value of x = 40

49. Given that the population has mean, L= 38 and Standard deviation 12. kle have to find the value of x Coyvesonding to each of the scores We know that, z score (z)= X-H That is z = X-H 20 = X-M x = 4 + Zo. use this formula to Calculate the value of x (a) z = 0.25 Then * = 4+ Z0 = 38+0.25x12) 38+3 = 41 Thus, the value of x= 41 (b) Z = -1.50 Then x = 4+ Zo = 38 + (-1.50 X 12) 38 +(-18) = 38-18 = 20 Thus, the value of x=20 -

(c) z=0.50 Then X = 4+ZO = 38 +0.5 X12) = 38+ 6 44 Thus, the value of x = 44 (d) Z-2.00 Then x = H+ zo = 38+ (2000X12) 38 + 24 = 62 Thus, the value of x = 62