Quantitative Methods 【Reading 9】Sample statements, following, normal

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Which of the following statements about the normal probability distribution is most accurate?

A) Five percent of the normal curve probability is more than two standard deviations from the mean.

B) Sixty-eight percent of the area under the normal curve falls between the mean and 1 standard deviation above the mean.

C) The normal curve is asymmetrical about its mean.

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The normal curve is symmetrical about its mean with 34% of the area under the normal curve falling between the mean and one standard deviation above the mean. Ninety-five percent of the normal curve is within two standard deviations of the mean, so five percent of the normal curve falls outside two standard deviations from the mean.

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Which of the following is least likely a probability distribution?

A) Roll an irregular die: p(1) = p(2) = p(3) = p(4) = 0.2 and p(5) = p(6) = 0.1.

B) Flip a coin: P(H) = P(T) = 0.5.

C) Zeta Corp.: P(dividend increases) = 0.60, P(dividend decreases) = 0.30.

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All the probabilities must be listed. In the case of Zeta Corp. the probabilities do not sum to one.

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Which of the following statements about probability distributions is least accurate?

A) A discrete random variable is a variable that can assume only certain clearly separated values resulting from a count of some set of items.

B) The skewness of a normal distribution is zero.

C) A binomial probability distribution is an example of a continuous probability distribution.

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The binomial probability distribution is an example of a discrete probability distribution. There are only two possible outcomes of each trial and the outcomes are mutually exclusive. For example, in a coin toss the outcome is either heads or tails.
The other responses are both correct definitions.

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Which of the following statements about probability distributions is least accurate?

A) In a binomial distribution each observation has only two possible outcomes that are mutually exclusive.

B) A probability distribution includes a listing of all the possible outcomes of an experiment.

C) A probability distribution is, by definition, normally distributed.

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Probabilities must be zero or positive, but a probability distribution is not necessarily normally distributed. Binomial distributions are either successes or failures.

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A probability distribution is least likely to:

A) contain all the possible outcomes.

B) give the probability that the distribution is realistic.

C) have only non-negative probabilities.

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The probability distribution may or may not reflect reality. But the probability distribution must list all possible outcomes, and probabilities can only have non-negative values.

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A dealer in a casino has rolled a five on a single die three times in a row. What is the probability of her rolling another five on the next roll, assuming it is a fair die?

A) 0.001.

B) 0.167.

C) 0.200.

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The probability of a value being rolled is 1/6 regardless of the previous value rolled.

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The number of ships in the harbor is an example of what kind of variable?

A) Indiscrete.

B) Continuous.

C) Discrete.

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A discrete variable is one that is represented by finite units.

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Which of the following is a discrete random variable?

A) The number of advancing stocks in the DJIA in a day.

B) The realized return on a corporate bond.

C) The amount of time between two successive stock trades.

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Since the DJIA consists of only 30 stocks, the answer associated with it would be a discrete random variable. Random variables measuring time, rates of return and weight will be continuous.

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Which of the following statements about probability distributions is most accurate?

A) A discrete uniform random variable has varying probabilities for each outcome that total to one.

B) A binomial distribution counts the number of successes that occur in a fixed number of independent trials that have mutually exclusive (i.e. yes or no) outcomes.

C) A continuous uniform distribution has a lower limit but no upper limit.

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Binomial probability distributions give the result of a single outcome and are used to study discrete random variables where you want to know the probability that an exact event will happen. A continuous uniform distribution has both an upper and a lower limit. A discrete uniform random variable has equal probabilities for each outcome.

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Assume a discrete distribution for the number of possible sunny days in Provo, Utah during the week of April 20 through April 26. For this discrete distribution, p(x) = 0 when x cannot occur, or p(x) > 0 if it can. Based on this information, what is the probability of it being sunny on 5 days and on 10 days during the week, respectively?

A) A positive value; infinite.

B) A positive value; zero.

C) Zero; infinite.

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The probability of it being sunny on 5 days during the week has some positive value, but the probability of having sunshine 10 days within a week of 7 days is zero because this cannot occur.