Answer:
76 ≤ B ≤ 89
Step-by-step explanation:
Mean score (μ) = 73.3
Standard deviation (σ) = 9.7
If B Scores are below the top 5% and above the bottom 62%, then:
62% ≤ B ≤ 95%
In a normal distribution, the 62nd percentile has a corresponding z-score of z = 0.305, while the 95th percentile has a corresponding z-score of z = 1.650.
The grades X1 and X2 which are the limits for a B grade are given by:
![z= \frac{X-\mu}{\sigma}\\0.305= \frac{X_1-73.3}{9,7}\\X_1=76.2\\1.650= \frac{X_2-73.3}{9,7}\\X_2=89.3](https://tex.z-dn.net/?f=z%3D%20%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%5C%5C0.305%3D%20%5Cfrac%7BX_1-73.3%7D%7B9%2C7%7D%5C%5CX_1%3D76.2%5C%5C1.650%3D%20%5Cfrac%7BX_2-73.3%7D%7B9%2C7%7D%5C%5CX_2%3D89.3)
Rounding to the nearest whole number, a B grade is given to grades between 76 and 89.