A psychology professor assigns letter grades on a test according to the following scheme. A: Top 6%6% of scores B: Scores below the top 6%6% and above the bottom 55U% C: Scores below the top 45E% and above the bottom 24$% D: Scores below the top 76v% and above the bottom 6%6% F: Bottom 6%6% of scores

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.

The numerical limits for a D grade is scores between 56 and 64.

Step-by-step 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.