Answer:
The limits for a D-score is (56 to 64) (nearest whole numbers)
Step-by-step explanation:
This is a binomial distribution problem with
Mean = μ = 70.9
Standard deviation = σ = 9.8
We will be using z-scores.
The z-score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ
The limits for a D-score: Scores below the top 76% and above the bottom 6%
Scores below the top 76% refer to the bottom 24% of the score.
Let the required limits be x' and x" & their z-scores be z' and z"
P(x' < x < x") = P(z' < z < z")
Representing this limits with inequalities.
Scores below the top 76% refer to the bottom 24% of the scores. The limit is P(x < x') = 0.24
Scores above the top 6%. The limit is P(x < x") = 0.06
Using the z-tables,
P(z < z') = 0.24
Gives a z-score of z' = -0.706
z = (x - μ)/σ
z' = (x' - μ)/σ
-0.706 = (x' - 70.9)/9.8
x' = (9.8)(-0.706) + 70.9 = 63.9812
P(z < z") = 0.06
z" = -1.555
z = (x - μ)/σ
z" = (x" - μ)/σ
-1.555 = (x" - 70.9)/9.8
x' = (9.8)(-1.555) + 70.9 = 55.661
The limits for a D-score is (55.661 to 63.9812)
Hope this Helps!!!