Suppose that customers arrive at a bank at a rate of 10 per hour. Assume that the number of customer arrivals X follows a Poisson distribution.

A. Find the probability of more than 25 people arriving within the next two hours using the Poisson mass function.

B. Find the probability of more than 25 people arriving within the next two hours using the normal approximation to the Poisson.

C. Compute the percent relative difference between the exact probability computed in part 1 and the normal approximation computed in part 2, i.e., 100 × (Approx−Exact)/Exact %. Comment on the adequacy of the approximation.

You are required to answer the FIVE (5) tasks below, in relation to your chosen organisation. For each task, you must fully justify your answer using evidence from your research.

Examine the relationship between the organisation’s corporate strategy and its operations strategy.

Analyse the importance of technology in supporting operations within the organisation

Discuss the rationale for the process types used in the organisation to manufacture the type of goods being created

Examine the role of performance measures in the organisation for driving improvements in operations.

Discuss the importance of agile and lean operations in continuing to meet the organisation’s customers’ needs.

At a certain bank, we have the following independent random samples of balances on the checks account statements for customers of two of its branches:

Determine the 90% confidence interval for the difference in balances at the two branches. Suppose the population standard deviations are equal.

With a 90% confidence level, you can ensure that the average balance in the North branch is greater than that of the South branch, being the difference between $ 67.70 and $ 232.30

An average of 10 cars per hour reaches an ATM with a single server that provides service without leaving the car. Suppose the time of average service for each client is 4 minutes, and how long the times between arrival and service times are exponential. Answer the following questions:
a) What is the notation for this problem?
b) What is the probability that the cashier is idle?
c) What is the average number of cars in the cashier's queue?
d) What is the average amount of time a customer spends in the parking lot of the bank (including service time)?
e) How many customers will the cashier serve on average per hour?

Suppose that you are the CEO of TrinketsNThings. Your sales operations manager has been experimenting with the price of a Trinket [x], in order to see how many Trinkets customers are willing to purchase in a week [y].

She gives you the following dataset:

Price of Trinket $3 $4 $5 $6

# of Trinkets Purchased (thousands) 19 15 12 8

*Calculate Cov(Price , # Purchased)

*Calculate Sx2

*What is the linear relationship between the price and quantity demanded of Trinkets? Calculate the relevant regression coefficient, then interpret this estimate in one or two sentences. For this answer, round to the nearest tenth.

1) A small regional carrier accepted 14 reservations for a particular flight with 13 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 42% chance, independently of each other.
Find the probability that overbooking occurs.  
Find the probability that the flight has empty seats.

2) The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 35 liters, and standard deviation of 4.7 liters.
What is the probability that daily production is between 29.4 and 31.3 liters?  (Round your answer to 4 decimal places.)

A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the Midwest and the West. The representative's belief is based on the results of a survey. The survey included a random sample of 760 midwestern residents and 680 western residents. 37% of the midwestern residents and 46% of the western residents reported that they were completely satisfied with their local telephone service. Find the 90% confidence interval for the difference in two proportions.

1. Find the point estimate that should be used in constructing the confidence interval.

2.  Find the margin of error. Round your answer to six decimal place

1) Describe what makes a cost “relevant” when making a decision between two alternatives.

2)Imagine you are a manager of a snack food company. You need to make a decision whether you should manufacture a new cheese curl or purchase it from another manufacturer and re-sell it to your customers.   Discuss what factors are relevant in this decision and how you would make the right decision.

3) What is a constraint in a manufacturing process? Why does it make sense to concentrate on contribution margin relative to the constrained resource instead of contribution margin per unit in these cases?

For each case below, graphically represent entities and relationships between entities. Include primary keys, foreign keys where appropriate. For each entity add a couple of attributes (fields) and then provide a brief statement explaining why each entity (table) is in 3NF.

An online retailer of coffee beans maintains a long list of unique coffee flavors. The company purchases beans from a number of suppliers; however, each specific flavor of coffee is purchased from only a single supplier. Many of the customers are repeat purchasers and typically order at least five flavors of beans in each order.

Kalokoni is a VAT registered trader. During the year to December 31, 2019, he bought
from a wholesaler grocery worth K9, 510 VAT exclusive. The wholesaler charges sales
tax at the prescribed rate of 16.5%. Kalokoni charged its customers on sale of the
groceries a price of K11, 200 VAT exclusive. Kalokoni also charged its customers VAT
on sales at 16.5%.
Required:

(i) Compute the VAT inclusive price that Kalokoni charged its customers on the
groceries.

(ii) Prepare the journal entries to record the sale of groceries in Kalokoni a’s general
ledger.

(iii) Calculate the input tax and output tax on Kalokoni’s purchase and sale of the
groceries.

(iv) How much VAT does Kalokoni pay to the government on the groceries
transactions above (1 mark)

(b) Kabisa commenced trading on 1 December 2018 as a distributor of the Straight Cut
garden lawn mower, a relatively new product which is now becoming increasingly
popular. Kabisa's purchases and sales of the Straight Cut garden lawn mower during the
three months ended 30 November 2019 are as follows:

Bought
January 1200 at K160 each
April 800 at K180 each.
October 1500 at K190 each

Sold.
June 1250 at k220 Each
November 2100 at k250 each.

Required:
From the following figures calculate the closing inventory-in-trade that would be shown
using;
(i) FIFO,
(ii) AVCO method on a perpetual inventory basis;
(iii) AVCO method on a simple inventory basis