I will be explaining problem # 3
3) In a recent contest, the mean score was 210, and the standard deviation was 25.
a) Find the z score of John who scored 190
b) Find the z score of Bill who scored 270.
c) If Mary had a z score of 1.25, what was Mary’s score?
Solving part (a)
X = 190, which is John’s score.
Next step is to plug in all the values and solve for z.
Z = 190 – 210/ 25 Ans: – 0.8
Solving part (b)
For part b, we have to follow the same exact steps as part a.
X = 270, which is Bill’s score.
Z = 270 – 210/ 25 Ans: 2.4
Solving part (c)
In part (c) the z score is given and we have to find the score. to find the score the formula we have to use is X = µ + zӨ
Mary’s z score is 1.25 and to find her score you have to solve for x.
x = 210 + (1.25)(25) Ans: 241.25