Question Continuation
F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 70.9 and a standard deviation of 9.8.
Find the numerical limits for a D grade.
Round your answers to the nearest whole number, if necessary.
Answer:
The numerical limits for a D grade is scores between 56 and 64.
Explanation:
Given.
D ranges between scores below the top 76% and above the bottom 6%
Mean, u = 70.9
Standard Deviation, σ = 9.8
To solve this, we'll calculate the numerical limits for (1) below the top 76% and (2) above the bottom 6%.
Calculating (1)
Using z = (x-u)/σ
Where p-value = 76% = 0.76
u = 70.9 and σ = 9.8
If the p-value = 0.76;
z-value = 1 - 0.76 = 0.24
From the z-table,
We have p(0.24) = -0.705.
Substitute these values in the above equation.
This gives.
-0.705 = (x - 70.9)/9.85 --- Solve for x
x - 70.9 = 9.85 * -0.705
x - 70.9 = -6.94425
x = 70.9 - 6.94425
x = 63.95575
x = 64 ---- Approximated
Calculating (2)
Using z = (x-u)/σ
Where p-value = 6% = 0.06
u = 70.9 and σ = 9.8
From the z-table,
We have p(0.06) = -1.555
Substitute these values in the above equation.
This gives.
-1.555 = (x - 70.9)/9.85 --- Solve for x
x - 70.9 = 9.85 * -1.555
x - 70.9 = -15.31675
x = 70.9 - 15.31675
x = 55.58325
x = 56 ---- Approximated
Hence, the calculated numerical limits for a D grade is scores approximately between 56 and 64.