0

# In a population of exam scores, a score of X = 85 corresponds to z = +2.0 and a score of X=61 corresponds to z = -1.00.

Q18. Find the mean for the population
Q19. Find the standard deviation (σ) for the population
Q20. What score (X) corresponds to a z = +0.8?
Q21. What score (X) corresponds to z = -1.64?
Q22. What proportion of the population (answer using 2 decimal places, e.g., 0.45, 0.21)
scored higher than X = 85?
Q23. What proportion of the population (answer using 2 decimal places, e.g., 0.45, 0.21)
scored higher than X = 61?

(I want to figure out the last 4 by myself but I just don't get how to do the first two... sorry if this is a dumb question.)

I would CERTAINLY have liked the problem to be stated as  "In a population of NORMALLY DISTRIBUTED exam scores....".   If the population is not normal,  and it is wrongly assumed to be so, the problem will give wrong answers!!!

### 1 Answer by Expert Tutors

Ryan S. | Mathematics and StatisticsMathematics and Statistics
4.8 4.8 (10 lesson ratings) (10)
0
This is not a dumb question at all. The first 2 questions are answered by solving a system of equations.

z=(x-μ)/σ
2=(85-μ)/σ
2σ=85-μ
μ+2σ=85   (1)

Similar steps for z = -1 and x = 61 gives:
μ-σ=61     (2)

Subtracting equation (2) from equation (1) gives:
3σ=24
σ=8

Substitute 8 for σ in equation (1) gives:
μ+16=85
μ=69