This is not the question, the correct question is:
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores.
Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer: The numerical limits for grade B is 81 and 92
Step-by-step explanation:
Given that
mean Ж = 79
Standard deviation S = 8.4
B: Scores below the top 6% and above the bottom 59%
To find the numerical value for Grade B
Below the top bottom 6% ( 0.06) is
p ( X < Ж ) = 1 - 0.06
p ( X < Ж ) = 0.94
therefore
P( (X - ц)/S < (X - Ж) / S)) = 0.94
(X - 79) / 8.4 = 1.5548 ( from normal distribution table )
X - 79 = 13.0603
X = 13.0603 + 79
X = 92.06 ≈ 92 ( nearest whole number)
Above bottom 59% ( 0.59) is
p ( X < Ж ) = 0.59
therefore
P( (X - ц)/S < (X - Ж) / S)) = 0.59
(X - 79) / 8.4 = 0.2275 ( from normal distribution table )
X - 79 = 1.9114
X = 1.9114 + 79
X = 80.91 ≈ 81 ( nearest whole number)
So the numerical limits for grade B is 81 and 92
