STATPRO HUMSS11-D W7 Review

Which of the following is not a property of a binomial random variable?

• The trials result can be classified into more than two outcomes.

• The trials are repeated.

• The probability of success remains constant from trial to trial.

• The probability of success remains constant from trial to trial.

Answer explanation

A Binomial random variable is involved in an experiment whose outcomes are classified as either a success or a failure.

The probability of success (p) for each trial is constant.

The probability of failure (1–p) for each trial is constant.

The experiment is performed in n identical and independent trials, and probabilities for success and failure are constant.

Which of the following random variables follows a hypergeometric distribution?

• The number of male students who prefer morning classes selected with replacement from a class.

• The number of male students selected without replacement from a class.

• The number of male students who prefer morning classes out of 20 students surveyed knowing that there's an average of 4 students who prefer morning classes.

• The number of male students to be asked before getting the 20th student who prefer morning classes.

Answer explanation

If the trials are dependent of each other and the total number of successes in a size sample are drawn without replacement from a finite population, then we have a hypergeometric distribution.

In the pmf of a Poisson random variable, which of the following is false?

• The occurrence or nonoccurrence of an event in one interval is independent of an occurrence on nonoccurrence of an event in any other interval.

Answer explanation

The Poisson probability distribution describes the number of times some event occurs during a specified interval. Evaluates the probability of a number of occurrences out of many opportunities in a region (period of time, area,

volume, weight, distance, other units of measurement). Each occurrence is independent of the others.

Which of the following is true?

• Counting the number of calls received by an office in one day is a binomial variable.

• Choosing a number of expired milk cans from 300 milk cans in storage, where 25 are known to be expired, is a hypergeometric variable.

• Taking a random sample size of 10 from a shipment of batteries in which 5% are defective and counting the number of defective units in the sample is a Poisson variable.

• Answering a 10-item multiple-choice test and counting the number of items answered correctly is a uniform variable.

Answer explanation

Refer to the properties of the mentioned discrete random variables.

The first game of the NBA Finals is a home court game for the Denver Heat. 85% of the fans attending it are Heat fans, while 15% are Miami Nuggets fans. Let X be the number of Heat fans selected.

If five fans are randomly selected, what is the probability that there are at most one Heat fan selected?

• 0.999

• 0.0001

• 0.9978

• 0.0022

Answer explanation

Scientific calculators are produced but 5% of the produced batch are defective. A gadget store owner ordered 20 of these calculators. The owner will inspect each gadget at a time and return it to the batch of 20 gadgets.

The store owner plans to order another batch of gadgets if there will be no defective item among the 20 gadgets upon inspection. What is the expected number of defective scientific calculators from this ordered batch?

• 2

• 10

• 0.5

• 1

In a student council meeting, seven out of ten votes support for a proposal to change the school uniform. Four student council officers were selected to form a small committee.

Let X be the number of officers who did not support the proposal.

What is the probability that more than one of the four randomly selected officers did not support the vote?

• 0.9667

• 0.3333

• 0.1667

• 0.8333

Answer explanation

Suppose that a HUMSS section is composed of 5 males and 10 females. Seven students were seleted without replacement, what is the probability that at least 3 males were in the selection?

• 0.8369

• 0.1631

• 0.0186

• 0.4267

Answer explanation

Let X be the number of selected males from the section.

On the average, an online seller receives 8 orders per day. If the number of orders follow a Poisson distribution, what is the probability that on a given day, the seller will receive exactly 5 orders?

• 0.0840

• 0.9160

• 0.9084

• 0.0916

Answer explanation

The average number of accidents at a particular intersection every year is 18. Assuming that the number of accidents is proportional to the number of years and that the accidents occur independently. What is the standard deviation of the number of accidents?

• 1.22

• 1.5

• 9

• 4.24