Chapter 4.3, Problem 50E

(a)

To determine

To calculate: The model using normal probability density function for a survey of college freshman class where the mean and standard deviation of height of females in the class is $64\text{ and }3.2$ inches respectively.

(b)

To determine

To graph: The sketch of the model obtained in part (a) for a survey of college freshman class where the mean and standard deviation of height of females in the class is $64\text{ and }3.2$ inches respectively.

(c)

To determine

To calculate: The derivative of the model obtained in part (a) for a survey of college freshman class where the mean and standard deviation of height of females in the class is $64\text{ and }3.2$ inches respectively.

(d)

To determine

To prove: The $f^{\prime }>0$ for $x<\mu$ and $f^{\prime }<0$ for $x>\mu$ of the derivative of the model obtained in part (c) for a survey of college freshman class where the mean and standard deviation of height of females in the class is $64\text{ and }3.2$ inches respectively.