Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. question 4: the times that a cashier spends proces

Question 4: The times that a cashier spends processing each person’s transaction are independent and identically distributed...

70.2K

Verified Solution

Question

Basic Math

Question 4:

The times that a cashier spends processing each person’stransaction are independent and identically distributed randomvariables with a mean of µ and a variance of σ2 . Thus,if Xi is the processing time for each transaction, E(Xi) = µ and Var(Xi) = σ2 .

Let Y be the total processing time for 100 orders: Y =X1 + X2 + · · · + X100

(a) What is the approximate probability distribution of Y , thetotal processing time of 100 orders? Hint: Y = 100X, where X = 1100 P100 i=1 Xi is the sample mean.

(b) Suppose for Z ∼ N(0, 1), a standard normal randomvariable:

P(a < Z < b) = 100(1 − α)%

Using your distribution from part (a), show that an approximate100(1 − α)% confidence interval for the unknown population mean µis:

(Y − 10bσ)/100 < µ < (Y − 10aσ)/100

(c) Now suppose that the population mean processing time isknown to be µ = 1.5 minutes, and the population standard deviationprocessing time is known to be σ = 1 minute. What is theprobability that it takes less than 120 minutes to process the 100orders? If you use R, please provide the commands used to determinethe probability. Could you show all steps in the hand writtenworking for this question please.

Answer & Explanation Solved by verified expert
3.6 Ratings (300 Votes)
We are given that for the random variable andAnd the random    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

For a sample containing both protein and nucleic acid, the absorbance measured at a particular wavelength...

Chemistry
Q

Consider an option on a non-dividend-paying stock when the stock price is $48, the exercise price...

Finance
Q

No smoking The General Social Survey conducted a poll of 653 adults in which the...

Statistics
Q

he graphs of y 2 sin z and y ave been plotted on the same...

Algebra
Q

NAME Factor each completely 21 5r x 6 23 3x 5x 12 25 66 29b...

Algebra
Q

Ann contributed 20,000 cash while Chok contributed 28,000 in cash and office equipment which cost...

Accounting
Q

Campbell Company, which sells electric razors, had $390,000 of cost of goods sold during the...

Accounting
Q

A partnership must separately report Section 1231 gains and losses rather than including them in...

Accounting
Q

***** Use the following data to answer the next two (2) questions** Gone Co. uses...

Accounting
Q

Use the trial balance shown below to prepare financial statements. Baman Consulting Trial Balance December...

Accounting
Q

The Vulcan Community Hospital purchased $1,500,000 worth of an MRI. The hospital paid $6,000 for...

Accounting
Q

Explain in detail THE CORRELATION BETWEEN THE EXXARO SHARE PRICE AND THE COAL PRICE

Finance