Statistics and Probability Answers

A recent study by the American Accounting Association revealed among 30 graduates in accounting 20 students graduating with a major in accounting select public accounting. Suppose we select a sample of 15 recent graduates.

A. What is the probability that exactly two select public accounting?

B. What is the probability that exactly five select public accounting?

A

child plays with a pair of scissors and

a piece of string 10 cm long. He cuts the string

into two at a randomly chosen place.

What is the probability that the piece of string to the left

of the pair of scissors is less than 4 cm long?

A hog raiser in a certain province uses two methods of pig-farming: intensive pig farming, where pigs are housed indoors in group housing or straw-lined sheds; and extensive pig farming, where pigs are allowed to wander around the farm or fence. Test the hypothesis whether or not the mean weight of pigs in intensive farming is better than the extensive farming based from the mean weight of the pigs in the sample with data shown below. Use a one-tailed test at x = 1%. Find the computed value of the test statistics.

Intensive farming: x₁=85 kg s = 10 kg

Extensive farming: x2= 79 kg s2 = 6 kg

ni 55

n2=45

Many things can contaminate urban storm water, including discarded batteries. When these batteries rupture, they discharge elements that are harmful to the environment. The sample mean zinc mass of 27 Panasonic AAA batteries was examined and found that it was 2.06g, with a sample standard deviation of 0.141g. Does this data provide compelling evidence for concluding that the population mean zinc mass exceeds 2.0g? Use a significance level α=0.05 to test the hypotheses.

Val wanted to know the average shearing strength, in pounds (lbs.), of a particular kind of rivet sold in a hardware store. He tested 20 rivets as samples and got the following results.

518

490

513

598

510

532

512

455

500

512

501

487

498

496

500

498

515

520

497

502

Construct a confidence interval for the population mean using 99% confidence.

A teacher conducted a study to know if blended leaming improves the students performances. A class of 25 students of Grade 11 was surveyed and found out that their mean score was 83 with a standard deviation of 3. A

study from other country revealed that = 80 with a standard deviation of 4. Test the hypothesis at 0.10 level of significance.

1. in building an arena, steel bars with a mean ultimate tenslie strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether or not there is no significant difference between the two means using a two-tailed with u = 0.01.

a. What are the appropriate hypotheses for the two-tailed test?

b. What is the test statistic to be used and the reasons for its selection? G. What is the critical value c?

d. What is the value of the test statistic or the computed value?

e. Formulate a conclusion about the given situation.

1. in building an arena, steel bars with a mean ultimate tenslie strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether or not there is no significant difference between the two means using a two-tailed with u = 0.01.

a. What are the appropriate hypotheses for the two-tailed test?

b. What is the test statistic to be used and the reasons for its selection? G. What is the critical value c?

d. What is the value of the test statistic or the computed value?

e. Formulate a conclusion about the given situation.

A population of values has a normal distribution with u = 56.1 and o = 57.7. If a random sample of size n = 20 is selected,

- Find the probability that a single randomly selected value is greater than 63.8. Round your answer to four decimals

P(X > 63.8) =

-Find the probability that a sample of size n = 20 is randomly selected with a mean greater than

P(M > 63.8) =

A population of values has a normal distribution with u = 91.9 and o = 38.4. A random sample of size n = 232 is drawn.

- What is the mean of the distribution of sample means? Ux=

-What is the standard deviation of the distribution of sample means? Round your answer to two decimal places. Ox=