STAT201 Quiz 5

A plumber has determined the possible number of house calls to be made each day, and their related probabilities. If the plumber charges a flat fee of $40 for a house call, the expected daily income is:

$70

To measure the success of the latest treatment for iPod-related deafness among young adults, researchers measured the sound sensitivity of 100 young adults by having them stand 20 feet away from a speaker playing "Slim Whitman Favorite Hits." It was found that 35% of the sample could not repeat any song lyrics from the CD. What is the mean of this distribution?

(100)(.35)

To measure the success of the latest treatment for iPod-related deafness among young adults, researchers measured the sound sensitivity of 100 young adults by having them stand 20 feet away from a speaker playing "Slim Whitman Favorite Hits." It was found that 35% of the sample could not repeat any song lyrics from the CD. What is the variance of this distribution?

(100)(.35)(.65)

The probability of success in any given trial of a binomial distribution is equal to?

1-q

Assume the statistics final is a multiple-choice exam with 50 questions, each question having 5 choices, only one of which is correct. Assume you answer all questions at random (guessing). The expected number of questions you would get correct would be:

10

bag contains 4 red marbles and 5 blue marbles. Two marbles are randomly drawn without replacement. Find the probability that both marbles are red.

12/72

Use the table below to find the mean of the probability distribution. x= 10,15,20 P(x)= .2,.5,.3

15.5

How many ways could you choose 4 successes from 10 trials of a binomial?

210

marketing researcher is tasked with asking consumers about their opinions of 7 different varieties of instant mashed potato. Knowing that the order of presentation might influence perceptions of taste, she wants to present unique orders of the products to consumers. To save some time in testing, the researcher decides that she will select only three of the seven products for each person to sample. How many unique orders of three out the seven will be used in her testing?

210

What is the value of the factorial for the number 4?

24

Use the table below to find the standard deviation of the probability distribution. As in the chapter example, your final result should be rounded to one decimal place but you will need to use up to 3 decimal places for your other calculations. x= 10,15,20 P(x)= .2,.5,.3

3.5

Suppose a family is randomly selected from among all families with 3 children. What is the probability that the family has exactly one boy? You may assume that Pr(boy) = Pr(girl) for each birth.

3/8

Suppose a family is randomly selected from among all families with 4 children. What is the probability that the family has exactly two boys? You may assume that Pr(boy) = Pr(girl) for each birth.

3/8

How many combinations of 3 items can be chosen from a set of 4 items?

4

Calculate (7) for a binomial experiment where = 10 and = 0.4.

4.25%

A marketing researcher is tasked with asking consumers about their opinions of 7 different varieties of instant mashed potato. Knowing that the order of presentation might influence perceptions of taste, she wishes to present all possible orders of the entire set of products. How many unique orders of the seven products are there?

5040

Think about the calculation of permutations. From a group of 7 items, how many ways are there to choose the first item?

7

The distribution of scores that are determined by multiple events are represented graphically as

A bell curve

A discrete random variable has a(n)_________ set of distinct possible values.

Countable

A discrete random variable has a____________ number of possible outcomes.

Countable

A permutation is a specific________of all or part of a set of n items.

Arrangement

A probability distribution of events with only two possible outcomes on each trial is a________ distribution.

Binomial

A distribution of events with only two possible outcomes in each trial is known as a________.

Binomial distribution

The number of ways of choosing k successes from n trials describes a___________.

Combination

Assume that the probability of a random person in the population having been to Chicago is .35. What is the probability that exactly three out of four people on an elevator will have been to Chicago?

.1115 or 11.15%

Ninety-four percent of California community college transfers feel that their community college adequately prepared them to handle upper-division coursework at their transfer university. We randomly survey 14 California community college transfers. We are interested in the number that feel that their community college adequately prepared them to handle upper division coursework at their transfer university. List the values that X, the Random Variable, may take on.

0, 1, 2, ..., 14

If X is binomial with n = 40 and p = .2 ( X ~ B ( 40 , 0.2 )) , find P ( X > 11 ) =

0.0875

A plumber has determined the possible number of house calls to be made each day, and their related probabilities. What is the probability that he makes at least 1, but no more than 3 house calls in a day?

0.80

The Fizz-Full Soda Company knows that 4% of the bottles of soda it produces are filled with less soda than required. If one purchases 10 bottles at random, the probability that at most 2 of these bottles will have less soda than required is:

0.9938

Suppose that a random variable has only two values, 0 and 1. If then what can we say about ?

E(X)= 0.5

What is the name for a variable that is followed by "!"?

Factorial

A biased coin could not be used in a probability experiment.

False

A set of n items will have more combinations possible than permutations.

False

A variable is random if each possible outcome has an equal likelihood.

False

An expected value of a random variable can never be negative.

False

Trials in a multinomial distribution have which of the following?

More than two possible outcomes

A distribution of events with more than two possible outcomes in each trial is known as a _________.

Multinomial distribution

Consider the following experiment. A particular car club has 100 members, 70 of which regularly wear their seat belts and 30 of which do not. Ten of these members are selected at random without replacement as they leave a car show. A given driver is considered a success if he or she is wearing a seat belt. The driver is considered a failure otherwise. Can we consider this experiment a binomial experiment?

No

If sampling without replacement occurs, do the picks follow the Binomial Distribution?

No, because the probability of success on each pick changes

A random variable is a_________ value representing the outcome of a probability experiment.

Numerical

A random variable is a__________description of each event in a sample space.

Numerical

The probabilities in a discrete probability distribution must sum to_________.

One

A marketing researcher is tasked with asking consumers about their opinions of 7 different varieties of instant mashed potato. Knowing that the order of presentation might influence perceptions of taste, she wishes to present all possible orders of the entire set of products. Does she need to be concerned with permutations or combinations?

Permutations

Which of the following are continuous random variables? (Select all that apply)

Reaction time to avoid a hazard in a driving simulator & Ounces of water consumed during a bout of exercise

An example of a continuous random variable is/are ________.

Temperature

Over the long run, which of the following will equal the expected value of a probability distribution?

The mean

The binomial coefficient represents which of the following?

The number of ways of choosing k successes from n trials

What does the symbol, P(x), represent?

The probability associated with a given outcome

The variance of a probability distribution is

The standard deviation squared

The expected value of a national lottery is likely to be negative.

True

The finishing positions of runners in a race would represent a permutation.

True

A continuous random variable has a(n)_________set of possible values.

Uncountable

Suppose that a random variable has only two values, 0 and 1. If P(X=0)=0.5 then what can we say about Var(X)?

Var(X)=0.25

Consider the following experiment. On a Friday night, a highway patrol officer sets up a roadblock and stops 100 drivers. A given driver is considered a success if he or she is wearing a seat belt; the driver is considered a failure otherwise. Can we consider this experiment a binomial experiment?

Yes

In 1938, Duke University researchers Pratt and Woodru conducted an experiment looking for evidence of ESP (extrasensory perception). In the experiment, students were presented with five standard ESP symbols (square, wavy lines, circle, star, cross). The experimenter shuffled a desk of ESP cards, each of which had one of the five symbols on it. The experimenter drew a card from this deck, looked at it, and concentrated on the symbol on the card. The student would then guess the symbol, perhaps by reading the experimenter's mind. This experiment was repeated with 32 students for a total of 60,000 trials. The students were correct 12,489 times. If the students were selecting one of the five symbols as random, the probability of success would be = 0.2 and we would expect the students to be correct 12,000 times out of 60,000. Should we write off the observed excess of 489 as nothing more than random variation?

Yes

Assume the statistics final is a multiple-choice exam with 50 questions, each question having 5 choices, only one of which is correct. Assume you answer all questions at random (guessing). Based upon numerical calculations, would you be surprised if a person got exactly half of the questions correct?

Yes, because the probability is almost 0

The mean of a binomial distribution is equal to_______.

n x p

An experiment is done in order to test the effectiveness of a new sleeping pill. Assuming that we have controlled for the placebo effect by using experimental and control groups, we can tell whether the pill is effective by whether or not the subjects in the experimental group fall asleep more quickly than those in the control group. The probability of failure in any given trial of this drug can be represented by the letter

q

The mean of a probability distribution can be found using the formula μ =_______.

∑ x P(x)

A criminologist wants to measure homicide in her city of 800,000 people. She might start by counting the number of recorded homicides among its citizens during the past year, which turns out to be 276. What type of variable is the number of homicides?

Discrete random

The number of heads in four flips of a coin is a(n)______?

Discrete random variable