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# Statistics - Random Variables - Sampling Distribution

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Problem 3-77

Suppose that 5 of a total of 20 company accounts are in error. An auditor selects a random sample of 5 out of the 20 accounts. Let X be the number of accounts in the sample that are in error. Is X binomial? If not, what distribution does it have? Explain. ...

Problem 5-74

The Toyota Prius uses both gasoline and electric power. Toyota claims its mileage per gallon is 52. A random sample of 40 cars is taken and each sample car is tested for its fuel efficiency. Assuming that 52 miles per gallon is the population mean and 2.4 miles per gallon is the population standard deviation, calculate the probability that the sample mean will be between 52 and 53. ...

Problem 6-83

A survey of 5,250 business travelers worldwide conducted by OAG Business Travel Lifestyle indicated that 91% of business travelers consider legroom the most important in-flight feature. (Angle of seat recline and food service were second and third, respectively.) Give a 95% confidence interval for the proportion of all business travelers who consider legroom the most important feature. ...

[See the Attached Questions File.]

https://brainmass.com/statistics/statistical-inference/statistics-random-variables-sampling-distribution-186498

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## Statistics and Probability

A retail grocer has decided to market organic "health food" and will purchase a new line of products from each of two suppliers. Unknown to the grocer, the two suppliers are in financial distress. Past experience has shown that, for firms with similar credit histories, the probability that bankruptcy will be initiated one year is .7. We are interested in observing the financial progress of the two supplies over the next year.

For this experiement, the simple events and their associated probabilites are as follows (B1: Supplier 1 declares bankruptcy; N1: Supplier 1 does not declare bankruprcy, etc.):

The Simple Events (B1, B2),(B1, N2),
(N1, B2) and (N1, N2) have probabilities equal to .49,.21,.21, and .09 respectively.

Compute the probabilities of each of the following events:

D: {Neither supplier declares bankruptcy during the next year}
F: {At least one supplier declares bankruptcy during the next year}

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