Question

In: Statistics and Probability

An entrepreneur opened a small hardware store in a street mall. During the first few weeks,...

An entrepreneur opened a small hardware store in a street mall. During the first few
weeks, business was slow with the store averaging only one customer arrived every 20
minutes. Assume that the random arrival of customers is Poisson distributed.


(a) What is the probability that exactly 5 customers arrive during one-hour period?


(b) If the average revenue from each customer is MYR 12, what is the probability
that the entrepreneur’s hourly earnings are at least MYR 24?


(c) If the hardware shop is open for 8 hours, what is the entrepreneurs mean daily
earnings if each customer were to spend on average about MYR 12.

( show steps please)

Solutions

Expert Solution

The random arrival of the customers follows a Poisson distribution.

Let x be the number of customers that arrive in 20 mins.

a) We are to find the probability that 5 customers arrive in one-hour.

The mean number of customers arriving in one hour = 3 customers (with one customer arriving in 20 minutes).

Therefore, we have

Therefore, the probability of this occuring is 0.1.

b) The average revenue for each customer is 12MYR. And on an average 3 customers are arriving in an hour. Therefore, the average revenue obtained in an hour will be 12*3 = 36MYR. Since the customer arrival follows a Poisson distribution, so will the revenue, with mean 36 MYR.

c) The mean per hour is 36MYR. The shop is open for 8 hours.

Hence the mean daily earning will be: 36*8 = 288 MYR.

orchestra answered 1 year ago
Next > < Previous

Related Solutions

An entrepreneur opened a small hardware store in a strip mall. During the first few weeks,...
An entrepreneur opened a small hardware store in a strip mall. During the first few weeks, business was slow, with the store averaging only one customer every 20 minutes in the morning. Assume that the random arrival of customers is Poisson distributed. (a) What is the probability that at least 1 hour would elapse between customers? (b) What is the probability that 10 to 30 minutes would elapse between customers? (c) What is the probability that less than 5 minutes...
Please write step by step in details thanks will upvote An entrepreneur opened a small hardware...
Please write step by step in details thanks will upvote An entrepreneur opened a small hardware store in a street mall. During the first few weeks, the business was slow with the store averaging only one customer arrived every 20 minutes. Assume that the random arrival of customers is Poisson distributed. (a) What is the probability that exactly 5 customers arrive during one-hour period? (b) If the average revenue from each customer is USD 12, what is the probability that...
Amy and Lester are the owners of The Hardware Store on main street in a large...
Amy and Lester are the owners of The Hardware Store on main street in a large town. Without consulting Amy, Lester hires an accountant to prepare a formal Balance Sheet, Income Statement, and Statement of Cash Flows for The Hardware Store. Amy understands the importance of having a Balance Sheet and Income Statement, but she does not understand the importance of having a Statement of Cash Flows. Amy reasons that examining the Cash account in the General Ledger is sufficient...
Amy and Lester are the owners of The Hardware Store on main street in a large...
Amy and Lester are the owners of The Hardware Store on main street in a large town. Without consulting Amy, Lester hires an accountant to prepare a formal Balance Sheet, Income Statement, and Statement of Cash Flows for The Hardware Store. Amy understands the importance of having a Balance Sheet and Income Statement, but she does not understand the importance of having a Statement of Cash Flows. Amy reasons that examining the Cash account in the General Ledger is sufficient...
During the first few weeks of the new television season, the evening news audience proportions were...
During the first few weeks of the new television season, the evening news audience proportions were recorded as: ABC = 31 5, CBS = 34%, NBC = 35%. A sample of 600 homes yielded the following viewing audience data. Channel Number of Homes ABC 150 CBS 200 NBC 250 We want to determine whether or not there has been a significant change in the percentage of viewing audience of the three networks. Conduct the appropriate hypothesis test at an alpha...
Globo opened its first store in 1992 and it is Canada's largest family shoe store with...
Globo opened its first store in 1992 and it is Canada's largest family shoe store with the widest selection of fashion-right footwear. The company has recently launched an online store. Sales via the internet have been sluggish compared to their brick and mortar stores, and management suspects that its regular customers have concerns regarding the security of online transactions. To determine if this is the case, they plan to survey a random sample of their regular customers. Under consideration are...
Jenna is working on the audit of a client’s accounts receivable. During the last few weeks,...
Jenna is working on the audit of a client’s accounts receivable. During the last few weeks, she has conducted interviews with the accounts receivable manager, the chief financial officer, and staff working in the accounts receivable department. She has overseen the external confirmations of accounts receivable, 30% of which required the recipient to respond whether or not the amount stated was correct. Jenna also inspected subsequent cash receipts from the client’s customers. She vouched a sample of accounts receivable balances...
Jenna is working on the audit of a client’s accounts receivable. During the last few weeks,...
Jenna is working on the audit of a client’s accounts receivable. During the last few weeks, she has conducted interviews with the accounts receivable manager, the chief financial officer, and staff working in the accounts receivable department. She has overseen the external confirmations of accounts receivable, 30% of which required the recipient to respond whether or not the amount stated was correct. Jenna also inspected subsequent cash receipts from the client’s customers. She vouched a sample of accounts receivable balances...
Jenna is working on the audit of a client’s accounts receivable. During the last few weeks,...
Jenna is working on the audit of a client’s accounts receivable. During the last few weeks, she has conducted interviews with the accounts receivable manager, the CFO, and staff working in the accounts receivable department. She has also overseen the external confirmations of accounts receivable, 70 percent of which required the recipient to respond as to whether or not the amount stated was correct. Jenna also conducted a review of subsequent cash receipts from the client’s customers. She vouched a...
Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove...
Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 55% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.) (a) at least 3 out of 5 business days (b) at least...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT