Statistical Software, Inc., offers a toll$-$free number where customers can call from $7$ A$.$M$.$ until $11$ P$.$M$.$ daily with problems involving the use of their products. It is impossible to have every call answered immediately by a technical representative, but it is important customers do not wait too long for a person to come on the line. Customers become upset when they hear the message $$Your call is important to us$.$ The next available representative will be with you shortly$$ too many times. To understand their process, Statistical Software decides to develop a control chart describing the total time from when a call is received until the representative answers the caller$$s question. Yesterday, for the $16$ hours of operation, four calls were sampled each hour. This information is reported on the next page, in minutes until a call was answered.

What are the Upper and Lower Control limits of the Range?

Time

$1$

$2$

$3$

$4$

$7$ A$.$M$.$

$8$

$9$

$15$

$4$

$8$ A$.$M$.$

$7$

$10$

$7$

$6$

$9$ A$.$M$.$

$11$

$12$

$10$

$9$

$10$ A$.$M$.$

$12$

$8$

$6$

$9$

$11$ A$.$M$.$

$11$

$10$

$6$

$14$

$12$ P$.$M$.$

$7$

$7$

$10$

$4$

$1$ P$.$M$.$

$10$

$7$

$4$

$10$

$2$ P$.$M$.$

$8$

$11$

$11$

$7$

$3$ P$.$M$.$

$8$

$11$

$8$

$14$

$4$ P$.$M$.$

$12$

$9$

$12$

$17$

$5$ P$.$M$.$

$7$

$7$

$9$

$17$

$6$ P$.$M$.$

$9$

$9$

$4$

$4$

$7$ P$.$M$.$

$10$

$12$

$12$

$12$

$8$ P$.$M$.$

$8$

$11$

$9$

$6$

$9$ P$.$M$.$

$10$

$13$

$9$

$4$

$10$ P$.$M$.$

$9$

$11$

$8$

$5$

Question $33$Answer

a$.$

$14\mathrm{.}12$ and $0$

b$.$

$13\mathrm{.}67$ and $6\mathrm{.}19$

c$.$

$2\mathrm{.}115$ and $0\mathrm{.}577$

d$.$

$13\mathrm{.}48$ and $0$