Answer:
The minimum score required for an A grade is 92.5.
Step-by-step explanation:
We are given that an art history 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 63% C: Scores below the top 37% and above the bottom 16% D: Scores below the top 84% and above the bottom 8% E: Bottom 8% of scores
Also, Scores on the test are normally distributed with a mean of 77.4 and a standard deviation of 9.6.
<em>Let X = Scores on a test</em>
So, X ~ N()
The z score probability distribution is given by;
Z = ~ N(0,1)
where, = population mean
= standard deviation
Now, we have to find the minimum score required for an A grade, i.e.; Top 6% of scores.
So, Probability that the test separate the top 6% of scores is given by;
P(X > x) = 0.06
P( > ) = 0.06
P(Z > ) = 0.06
So, the critical value of x in z table which separate the top 6% is given as 1.5722, which means;
= 1.3543
= 77.4 + 15.09312 = 92.5
Therefore, minimum score required for an A grade that represent top 6% of scores is 92.5.