A certain large shipment comes with a guarantee that it contains no more than 20% defective items. If the proportion of items in the shipment is greater than 20%, the shipment may be returned. You draw a random sample of 10 items and test each one to determine whether it is defective. Assume

p(x >=2) = 1- (p(0) +p(1))

= 1- (0.1074 + 0.2684)

= 0.6242

5.             based on the above, if 20% of the items in the shipment are defective, would 2 defectives in a sample of 10 be an unusually large number?
6.              If you found that 2 of 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.
7.             Find the variance, σ2=
8.               Find the standard deviation, σ=

The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.2. Suppose you purchase box after box until you have obtained four of these prizes.

(a)

What is the probability that you purchase x boxes that do not have the desired prize?

h(x; 4, 0.2)

b(x; 4, 2, 10)

nb(x; 4, 2, 10)

b(x; 4, 0.2)

h(x; 4, 2, 10)

nb(x; 4, 0.2)

(b)

What is the probability that you purchase six boxes? (Round your answer to four decimal places.)

.256

(c)

What is the probability that you purchase at most six boxes? (Round your answer to four decimal places.)

(d)

How many boxes without the desired prize do you expect to purchase?

How many boxes do you expect to purchase?

Given two random variables x and y

State of Nature   Probability   variable x   variable y

I 0.2 18 0

II 0. 2 5 -3

III 0.2 12 15

IV 0.2 4 12

V 0.2 6 1

(i) Calculate the mean and variance of each of these variables and the covariance between them

(ii) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following part folios.

% in x 125 100 75 50 25 0 -25

% in y -25 0 25 50 75 100 125

(iii)Find the portfolio that has the minimum variance.

(iv)Let portfolio A have 75% in x and portfolio B has 25% in x. Calculate the covariance between the two portfolios.

(v) Calculate the covariance between the minimum variance portfolio and portfolio A.

Test the following hypotheses by using the χ ² goodness of fit test.

A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C. Use  = .01 and test to see whether the proportions are as stated in H₀. Use Table 12.4.

a. Use the p-value approach.

χ ² =  (to 2 decimals)

The p-value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2

Conclusion:
SelectConclude the proportions differ from 0.2, 0.4, and 0.4.Cannot conclude that the proportions differ from 0.2, 0.4, and 0.4.Item 3

b. Repeat the test using the critical value approach.

χ ² _.01 =  (to 3 decimals)

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs $7,000 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

BPC has decided to evaluate the riskier project at 13% and the less-risky project at 9%.

1. What is each project's expected annual cash flow? Round your answers to two decimal places.

   Project A $

   Project B $

   Project B's standard deviation (σ_B) is $5,426 and its coefficient of variation (CV_B) is 0.71. What are the values of (σ_A) and (CV_A)? Round your answer to two decimal places.

   σ_A = $

   CV_A =

PROJECT RISK ANALYSIS

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs $6,750 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

BPC has decided to evaluate the riskier project at 11% and the less-risky project at 10%.

1. What is each project's expected annual cash flow? Round your answers to two decimal places.

   Project A $

   Project B $

   Project B's standard deviation (σ_B) is $6,158 and its coefficient of variation (CV_B) is 0.78. What are the values of (σ_A) and (CV_A)? Round your answer to two decimal places.

   σ_A = $

   CV_A =

The Butler-Perkins Company (BPC) must decide between two mutually exclusive projects. Each costs $7,000 and has an expected life of 3 years. Annual project cash flows begin 1 year after the initial investment and are subject to the following probability distributions:

BPC has decided to evaluate the riskier project at 11% and the less-risky project at 10%.

1. What is each project's expected annual cash flow? Round your answers to two decimal places.

   Project A $

   Project B $

   Project B's standard deviation (σ_B) is $5,776 and its coefficient of variation (CV_B) is 0.74. What are the values of (σ_A) and (CV_A)? Round your answer to two decimal places.

   σ_A = $

   CV_A =

plase help!

Thank you!

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was four minutes. Use that as a planning value for the standard deviation in answering the following questions. a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 69 seconds, what sample size should be used? Assume 95% confidence. b. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was four minutes. Use that as a planning value for the standard deviation in answering the following questions.

a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 69 seconds, what sample size should be used? Assume 95% confidence.

b. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

The Starr Theater, owned by Meg Vargo, will begin operations in March. The Starr will be unique in that it will show only triple features of sequential theme movies. As of March 1, the ledger of Starr showed: Cash $2,950, Land $22,000, Buildings (concession stand, projection room, ticket booth, and screen) $10,000, Equipment $10,000, Accounts Payable $6,000, and Owner’s Capital $38,950. During the month of March, the following events and transactions occurred.

1.) Enter the beginning balances in the ledger.

2.) Journalize the March transactions. Starr records admission revenue as service revenue, rental of the concession stand as rent revenue, and film rental expense as rent expense.(Credit account titles are automatically indented when the amount is entered. Do not indent manually. Record journal entries in the order presented in the problem. If no entry is required, select "No Entry" for the account titles and enter 0 for the amounts.)

3.) Post the March journal entries to the ledger. (Post entries in the order of journal entries presented in the previous question.)