Question 1

The expected value of a binomial distribution is expressed as np, where n equals the number of trials and p equals the probability of success of any individual trial.

Accepted Answer

This is true according to the formula for expected value in a binomial distribution, which is E(X) = np, where n is the number of trials and p is the probability of success on any individual trial.

Question 2

A new young executive is perplexed at the number of interruptions that occur due to employee relations.She has decided to track the number of interruptions that occur during each hour of her day.Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day.The data is shown below.
  On average, she should expect 1.0 interruptions per hour.

Accepted Answer

The data shows that between 0 and 3 interruptions occur during any given hour of her day. The average of this range is 1.0 interruption per hour, which means that on average, she should expect 1.0 interruption per hour. Therefore, the statement "On average, she should expect 1.0 interruptions per hour" is true.

Question 3

The variance of a binomial distribution is expressed as np/(1 - p), where n equals the number of trials and p equals the probability of success of any individual trial.

Accepted Answer

The variance of a binomial distribution is expressed as np(1 - p), where n equals the number of trials and p equals the probability of success on any individual trial.

Question 4

Assume you have a normal distribution representing the likelihood of completion times.The mean of this distribution is 10, and the standard deviation is 3.The probability of completing the project in 8 or fewer days is the same as the probability of completing the project in 18 days or more.

Accepted Answer

We need to find the z-scores for 8 and 18 days using the formula z = (x - mu) / sigma, where x is the value (8 or 18), mu is the mean (10), and sigma is the standard deviation (3).
For 8 days, z = (8 - 10) / 3 = -0.67
For 18 days, z = (18 - 10) / 3 = 2.67
Using a standard normal table or calculator, we find that the probability of z being less than -0.67 is 0.2514 and the probability of z being greater than 2.67 is 0.0035. Therefore, the probability of completing the project in 8 or fewer days is 0.2514 and the probability of completing the project in 18 days or more is 0.0035. These probabilities are not the same, so the answer is B (False).

Question 5

The F statistic is the ratio of two sample standard deviations from independent normal distributions.

Accepted Answer

The F statistic is the ratio of two sample variances, not standard deviations.

Question 6

Bayes' theorem is used to calculate

Accepted Answer

Bayes' theorem is used to calculate revised probabilities by incorporating new information into prior probabilities.

Question 7

The F distribution is a continuous probability distribution that is helpful in testing hypotheses about variances.

Accepted Answer

The F distribution is indeed a continuous probability distribution commonly used for hypothesis testing involving variances.

Question 8

The mean and standard deviation of the Poisson distribution are equal.

Accepted Answer

The answer of The mean and standard deviation of the...

Question 9

Suppose that we determine the probability of a warm winter based on the number of warm winters experienced over the past 10 years.In this case, we have used

Accepted Answer

The probability based on the number of warm winters experienced in the past 10 years is calculated using relative frequency. Relative frequency refers to the number of times an event occurs divided by the total number of trials. In this case, the event is having a warm winter and the total number of trials is the past 10 winters.

Question 10

The standard deviation equals the square of the variance.

Accepted Answer

The standard deviation equals the square root of the variance, not the square.

Question 11

Subjective probability assessments depend on

Accepted Answer

Subjective probability assessments are based on personal experience and judgment, making D the best choice. While the other options may play a role in objective probability assessments, they do not apply to subjective probability assessments.

Question 12

Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same.What is the probability that one of the first three golfers that registered for the tournament will win?

Accepted Answer

The probability of any one of the ten golfers winning is 1/10. The probability of the first three golfers registered winning is (3/10) * (1/9) * (1/8) = 0.00347. However, since we only need one of them to win, we can multiply this probability by 3 (for the three possible first place winners) and then subtract the probability that none of the first three golfers win (which is (7/10) * (6/9) * (5/8) = 0.4375) to get: 3 * 0.00347 - 0.4375 = 0.300. Therefore, the probability that one of the first three golfers registered will win is 0.300 or 30%.

Question 13

If P(A)= 0.3, P(B)= 0.2, P(A and B)= 0.0, what can be said about events A and B?

Accepted Answer

If P(A and B)=0, then events A and B cannot occur at the same time, and therefore are mutually exclusive. If events A and B were independent, then P(A and B)=P(A)P(B), which is not the case here. The terms "posterior probabilities" and "collectively exhaustive" are not applicable to this scenario.

Question 14

A new young executive is perplexed at the number of interruptions that occur due to employee relations.She has decided to track the number of interruptions that occur during each hour of her day.Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day.The data is shown below.
  On average, she should expect 0.8 interruptions per hour.

Accepted Answer

The average number of interruptions per hour over the last month is less than 1 (0.8), so on average, she should expect less than 1 interruption per hour.

Question 15

A conditional probability P(B|A)is equal to its marginal probability P(B)if

Accepted Answer

If statistical independence exists, it means that the occurrence of event A does not affect the probability of event B, in which case P(B|A) = P(B). So the marginal probability of B is equal to its conditional probability given A if and only if A and B are statistically independent.

Question 16

In a normal distribution, the Z value represents the number of standard deviations from a value X to the mean.

Accepted Answer

This statement is true. The Z value, also known as the standard score, represents the number of standard deviations a particular value (X) is from the mean in a normal distribution.

Question 17

Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same.Six of the entrants are female and two of those are engineering majors.Three of the men are engineers.What is the probability that the winner will be either female or majoring in something other than engineering?

Accepted Answer

Total number of entrants = 10
Number of females = 6
Number of female engineers = 2
Number of male engineers = 3
Therefore, the number of entrants who are not female or engineering majors = 10 - 6 - 2 - 3 = 1
The probability of the winner being female or majoring in something other than engineering = (6/10) + (1/10) = 0.7, so the best choice is (C).

Question 18

Assume you have a normal distribution representing the likelihood of completion times.The mean of this distribution is 10, and the standard deviation is 3.The probability of completing the project in 7 or fewer days is the same as the probability of completing the project in 13 days or more.

Accepted Answer

In a normal distribution, the probabilities on either side of the mean at equal distances are the same. Since 7 is 3 units below the mean (10) and 13 is 3 units above the mean, the probabilities of completion times less than 7 days and more than 13 days are equal.

Question 19

The probability of obtaining specific outcomes in a Bernoulli process is described by the binomial probability distribution.

Accepted Answer

The binomial probability distribution is associated with the number of successes in a fixed number of Bernoulli trials.

Question 20

If the sale of ice cream and pizza are independent, then as ice cream sales decrease by 60 percent during the winter months, pizza sales will

Accepted Answer

The fact that the sales of ice cream and pizza are independent means that they do not affect each other. Therefore, a decrease in ice cream sales will have no effect on pizza sales. Thus, the answer is D, pizza sales will be unrelated.

Quiz 2: Probability Concepts and Applications