Question

In: Math

A toll-free phone number is available from 9 a.m. to 9 p.m. for your customers to...

A toll-free phone number is available from 9 a.m. to 9 p.m. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 1.0 calls are received per minute. Complete parts (a)through (c).


A.    what is the probability that during a 1 min period zero phone calls will be received?

B.    what is the probability that during a 1 min period three or more phone calls will be received?

C.    what is the maximum number of phone calls that will be received in a 1 min period 99.99% of the time?

Solutions

Expert Solution

a) the probability that during a​ 1-minute period zero phone calls will be​ received is,

P(k=0)=e-1 *(10 /0!)=e-1 =0.3679

Excel function:

P(k=0)=POISSON(0,1,FALSE)=0.3679

b) the probability that during a​ 1-minute period three or more phone calls will be​ received is,

P(k>=3)=1-e-1 *( 10/0!+11/1!+12/2!)

                 =1-0.3679(1+1+0.5)

                 =1-0.3679*2.5

                  =1-0.9197

                  =0.0803

Excel function:

P(k>=3)=1-POISSON(2,1,TRUE)=0.0803

c) maximum number of phone calls that will be received in a​ 1-minute period​ 99.99% of the​ time is,

No. of calls(x) POISSION(x,1,TRUE)
3 0.9810
4 0.9963
5 0.9994
6 0.9999
7 1.0000
8 1.0000

Hence,maximum number of calls is 6 in a 1 minute period 99.99% of the time.

Please upvote my answer if you like..


Related Solutions

A toll-free phone number is available from 9 a.m. to 9 p.m. to customers who want...
A toll-free phone number is available from 9 a.m. to 9 p.m. to customers who want to register a complaint about a product purchased from your company. Past history indicates that, on average, 0.4 calls are received per hour. (a) Decide what would be an appropriate distribution to describe the process [2] of people making complaints. Give a justification of your answer, in at most one sentence. (b) Using the distribution in (a), find the following probabilities: (i) the probability...
A toll-free phone number is available from 9 AM to 9 PM for your customers to...
A toll-free phone number is available from 9 AM to 9 PM for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 2.8 calls is received per minute. What is the area of opportunity?
Club Fitness is open from 5 A.M. until 9 P.M. Monday through Saturday. The gym is...
Club Fitness is open from 5 A.M. until 9 P.M. Monday through Saturday. The gym is closed on Sundays and holidays. Hank Hunkley, the owner, is considering offering 24-hour, 7-day-a-week, 365-days-a year access for an additional $59 a year per member. In exchange for the extra fee, the member would receive a magnetic fob that will unlock the door when the facility is closed. Each fob would cost Hank $5. Based on a survey taken of his 951 current members,...
Q31. A customer comment phone line is staffed from 8:00 a.m. to 4:30 p.m. five days...
Q31. A customer comment phone line is staffed from 8:00 a.m. to 4:30 p.m. five days a week. Records are available that show the number of calls received every day for the last five weeks. Excel Data can be found in Data Tab/Sheet a. Show a time series data plot of data and describe your observation in terms of pattern, trend, etc. b. Use a dummy variable method forecasting method to produce Week 6’s Daily and total calls for Week...
C&A makes two types of products using four machines from 9 a.m. to 5 p.m. each...
C&A makes two types of products using four machines from 9 a.m. to 5 p.m. each day. Product A visits machines 1, 2, and 4. Product B only visits machines 1 and 3. The capacity is 0.4 unit per minute at machine 1, 0.12 unit per minute at machine 2, 0.2 unit per minute at machine 3, and 0.3 unit per minute at machine 4. The demand per day is 40 units for Product A and 160 units for Product...
An IV of 1,000 mL is to infuse from 6 a.m. until 2 p.m. The drop...
An IV of 1,000 mL is to infuse from 6 a.m. until 2 p.m. The drop factor is 15 gtt/mL. Calculate the flow rate.__________    At 11 a.m. you notice that 750 mL has infused. Recalculate the flow rate for the remaining solution. _____________ Does it fall within the safe range for recalculating an IV flow rate? ________
An IV of 1,000 mL is to infuse from 6 a.m. until 2 p.m. The drop...
An IV of 1,000 mL is to infuse from 6 a.m. until 2 p.m. The drop factor is 15 gtt/mL. Calculate the flow rate
The data to the right represent the number of customers waiting for a table at?6:00 P.M....
The data to the right represent the number of customers waiting for a table at?6:00 P.M. for 40 consecutive Saturdays at? Bobak's Restaurant. Complete parts?(a) through? (h) below. 5 9 3 4 9 5 4 3 11 10 4 6 2 5 3 7 7 11 6 2 6 4 5 8 13 10 8 2 7 5 5 10 6 10 4 6 3 5 8 4 Number of Customers Frequency 1–3 7 4–6 18 7-9 8 10–12 6...
Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free...
Skyline pizza is a famous restaurant operating a number of outlets. The restaurant uses a toll-free telephone number to book pizzas at any of its outlets. If the clerk is occupied on one line, incoming phone calls to the restaurant are answered automatically by an answering machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls come in at a rate of about 15 per...
The Schmedley Discount Department Store has approximately 300 customers shopping in its store between 9 A.M....
The Schmedley Discount Department Store has approximately 300 customers shopping in its store between 9 A.M. and 5 P.M. on Saturdays. In deciding how many cash registers to keep open each Saturday, Schmedley’s manager considers two factors: customer waiting time (and the associated waiting cost) and the service costs of employing additional checkout clerks. Checkout clerks are paid an average of $8 per hour. When only one is on duty, the waiting time per customer is about 10 minutes (or...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT