Search 74,259 tutors
FIND TUTORS
Ask a question
0 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.)
 

Comments

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!!! 
Tutors, please sign in to answer this question.

1 Answer

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

Woodbridge statistics tutors