Question

In: Statistics and Probability

A firm gives discounts to its customers who pay their bills on time. A customer receives...

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the expected number of customers that will take the discount (round answers to three decimal places, for example, 0.xxx)?

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that at least three take the discount (round answers to three decimal places, for example, 0.xxx)?

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that exactly three take the discount (round answers to three decimal places, for example, 0.xxx)?

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that less than three take the discount (round answers to three decimal places, for example, 0.xxx)?

Solutions

Expert Solution

Let , X be the number of customer use the discount.

Here , the X has a binomial distribution with parameter n=8 and p=030

Now ,q=1-p=0.70

The probability mass function of X is ,

= 0 ; otherwise

a) E(X)=np=8*0.30=2.400

Therefore , the expected number of customers that will take the discount is 2.400

b)

; From binomial distribution probability table

Therefore , the probability that at least three take the discount is 0.448

c)

  ; From binomial distribution probability table

Therefore , the probability that exactly three take the discount is 0.254

d)

; From binomial distribution probability table

Therefore , the probability that less than  three take the discount is 0.552

orchestra answered 2 years ago
Next > < Previous

Related Solutions

A firm currently sells its product with a 2% discount to customers who pay by cash...
A firm currently sells its product with a 2% discount to customers who pay by cash or credit card when they purchase one of the firm's products; otherwise, the full price is due within 30 days. Forty percent (40%) of customers take advantage of the discount. The firm plans to drop the discount so the new terms will simply be net 30. In doing so it expects to sell 100 fewer units per month and all customers to pay at...
Pay your bills: In a large sample of customer accounts, a utility company determined that the...
Pay your bills: In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 29 with a standard deviation of 5 days. Assume the data to be approximately bell-shaped. 1) Estimate the percentage of bills for which payment was made in greater than 34 days. Approximate what percent of the bills have payments greater than 34.
Pay your bills. In a large sample of 250 customer accounts, a In a large sample...
Pay your bills. In a large sample of 250 customer accounts, a In a large sample of 250 customer accounts, a utility company determined that the average number of days between when the bill was sent out and when the payment was made is 32 with a standard deviation of 7 days. Assume the data to be approximately bell- shaped. Use the empirical rule to construct a diagram of the distribution of the data. Between what two numbers will approximately...
A1 (a) Bank Muscat collect bills for encashment on behalf of its customers. It is a...
A1 (a) Bank Muscat collect bills for encashment on behalf of its customers. It is a part of its secondary functions. During the year 2019 it received bills for collection amounting to OMR 2,000,000. The balance on bills for collection on 31/12/2018 amounted to OMR 200,000. It returned the dishonoured bills to its customers amounting to OMR 25,000. Bills collected during the year amounted to OMR 850,000. Record these transactions in the journal and prepare the ledger for the same....
Grand Opening Bank is offering a​ one-time investment opportunity for its new customers. A customer opening...
Grand Opening Bank is offering a​ one-time investment opportunity for its new customers. A customer opening a new checking account can buy a special savings bond for ​$600 ​today, which the bank will compound at 8​% for the next ten years. The savings bond must be held for at least five​ years, but can then be cashed in at the end of any year starting with year five. What is the value of the bond at each​ cash-in date up...
Grand Opening Bank is offering a​ one-time investment opportunity for its new customers. A customer opening...
Grand Opening Bank is offering a​ one-time investment opportunity for its new customers. A customer opening a new checking account can buy a special savings bond for ​$800 ​today, which the bank will compound at 5.5​% for the next ten years. The savings bond must be held for at least five​ years, but can then be cashed in at the end of any year starting with year five. What is the value of the bond at each​ cash-in date up...
What are different methods to encourage customers/clients to pay their bills timely or even quicker? How...
What are different methods to encourage customers/clients to pay their bills timely or even quicker? How can we use receivables to get our hands on cash before we collect the receivable? What do you do if a customer won't pay their amount due?
Your company currently sells its product with a 3% discount to customers who pay cash immediately....
Your company currently sells its product with a 3% discount to customers who pay cash immediately. Otherwise the full price is due within 30 days. Half of your customers take advantage of the discount. You are considering dropping the discount so that your new terms would just be net 30. If you do that, you expect to lose some customers who were only willing to pay the discounted price, but the rest will simply switch to taking the full 30...
Apple produces widgets and bills customers following a time and materials approach. Apple reports the following...
Apple produces widgets and bills customers following a time and materials approach. Apple reports the following budgeted information for 2016: Direct materials: Direct materials used:                             $250,000 Direct materials overhead                      $40,000 Direct materials profit                            15% Labor: Direct labor                                             $450,000 Direct labor overhead                             $110,000 Direct labor hours                                   20,000 hours Direct labor profit:                                  $7.00 per hour On January 1, 2016, a customer requests an estimate from Apple on a job. Apple makes the following assumptions regarding the job: Direct labor hours:                      200 Direct materials used:                 $7,000 Using the information above, calculate the...
Why must amounts received in advance from customers be deferred? a. The customer may not pay...
Why must amounts received in advance from customers be deferred? a. The customer may not pay the entire balance due b. The company receiving payment has not earned the amount c. The customer has a right of return d. All of the above are reasons to defer
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT