An art history professor assigns letter grades on a test according to the following scheme. A: Top 5% of scoresB: Scores below the top 5% and above the bottom 62%C: Scores below the top 38% and above the bottom 22%D: Scores below the top 78% and above the bottom 5%F: Bottom 5% of scoresScores on the test are normally distributed with a mean of 73.3 and a standard deviation of 9.7. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.

Grade B score:

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 73.3

Standard Deviation, σ = 9.7

We are given that the distribution of score on test is a bell shaped distribution that is a normal distribution.

Formula:

B: Scores below the top 5% and above the bottom 62%

We have to find the value of x such that the probability is 0.62

Calculation the value from standard normal z table, we have,  

We have to find the value of x such that the probability is 0.05

Calculation the value from standard normal z table, we have,  

Thus, the numerical value of score to achieve grade B is