Chapter 15.8, Problem 25P

As in Examples 1 and 2, use (a) the binomial distribution; (b) the corresponding normal approximation, to find the probabilities f each of the following:

An instructor who grades “on the curve” computes the mean and standard deviation of the grades, and then, assuming a normal distribution with this $\mu$ and $\sigma ,$ sets the border lines between the grades at: $\text{C}$ from $\mu -\frac{1}{2}\sigma$ to $\mu +\frac{1}{2}\sigma ,\text{B}$ from $\mu +\frac{1}{2}\sigma$ to $\mu +\frac{3}{2}\sigma ,$ A from $\mu +\frac{3}{2}\sigma$ up, etc. Find the percentages of the students receiving the various grades. Where should the border lines be set to give the percentages: $\text{A}$ and $\text{F},10\%;\text{B}$ and $\text{D},20\%;\text{C},40\%?$