Chapter 4.3, Problem 49E

(a)

To determine

To calculate: The model using normal probability density function for the mean SAT score for college bound seniors where the mean and standard deviation of mathematics portion was $513\text{ and }120$ respectively.

(b)

To determine

To graph: The sketch of the model obtained in part (a) for the mean SAT score for college bound seniors where the mean and standard deviation of mathematics portion was $513\text{ and }120$ respectively.

(c)

To determine

To calculate: The derivative of the model obtained in part (a) for the mean SAT score for college bound seniors where the mean and standard deviation of mathematics portion was $513\text{ and }120$ 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 the mean SAT score for college bound seniors where the mean and standard deviation of mathematics portion was $513\text{ and }120$ respectively.