Chapter 8, Problem 41RE

(a)

To determine

To calculate: The probability distribution, expected value, and the standard deviation of the random variable X if X is the number of orders per million residents in U.S. city selected randomly, and the count of online orders at OHaganBooks.com per million residents in $1$ month in $100$ U.S. cities is shown in the table.

Orders per million residents	$1-2.9$	$3-4.9$	$5-6.9$	$7-8.9$	$9-10.9$
Number of cities	$25$	$35$	$15$	$15$	$10$

(b)

To determine

To calculate: The range of orders per million residents from approximately $68\%$ of cities using empirical rule if X is the number of orders per million residents in U.S. city selected randomly, and the count of online orders at OHaganBooks.com per million residents in $1$ month in $100$ U.S. cities is shown in the table. Also, determine whether empirical rule can be applied or not.

Orders per million residents	$1-2.9$	$3-4.9$	$5-6.9$	$7-8.9$	$9-10.9$
Number of cities	$25$	$35$	$15$	$15$	$10$

(c)

To determine

The actual percentage of cities from which between $3$ and $8$ orders per million residents is obtained out of the following options, if X is the number of orders per million residents in U.S. city selected randomly, and the count of online orders at OHaganBooks.com per million residents in $1$ month in $100$ U.S. cities is shown in the table. Also, determine whether empirical rule can be applied or not.