Reading 9: Common Probability Distributions - LOS a ～ Q6-9

答案和详解如下：

6、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 is, by definition, normally distributed.

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

D)   One of the key properties of a probability function is  0 ≤ p ≤ 1.

The correct answer was B)

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

7、Which of the following statements about probability distributions is FALSE?

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

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

C)   A continuous random variable is a quantity resulting from a random experiment that by chance can assume an infinite number of different values.

D)   The skewness of a normal distribution is zero.

The correct answer was A)

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 all correct definitions.

8、Which of the following is NOT a probability distribution?

A)   Flip a coin: P(H)=P(T)=0.5.

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

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

D)   DJIA: P(increase)=0.67, P(not increase)=0.33.

The correct answer was C)    

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

9、Which of the following statements about the normal probability distribution is TRUE?

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

B)   The normal curve is asymmetrical about its mean.

C)   The standardized normal distribution has a mean of zero and a standard deviation of 10.

D)   Sixty-eight percent of the area under the normal curve falls between 0 and +1 standard deviations above the mean.

The correct answer was A)

The normal curve is symmetrical with a mean of zero and a standard deviation of 1 with 34% of the area under the normal curve falling between 0 and + 1 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.