STAT EXAM #2

The probability distribution for the number of goals the Lions soccer team makes per game is given below. 0 - 0.15 1 - 0.30 3 - 0.05 3 - 0.35 4 - 0.15 What is the probability that in a given game the Lions do not score more than 2 goals?

0.50

Consider the bivariate distribution for the random variables x and y. The expected value of a linear combination of x and y is

E(ax + by) = aE(x) + bE(y)

If A and B are independent events with P(A) = 0.1 and P(B) = 0.6, then

P(A ∩ B) = 0.06

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called the counting rule for

permutations

A description of the distribution of the values of a random variable and their associated probabilities is called a

probability distribution

A numerical description of the outcome of an experiment is called a

random variable

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the _____ method.

relative frequency

A method of assigning probabilities based upon judgment is referred to as the _____ method.

subjective

Which of the following is a required condition for a discrete probability function?

Σf(x) = 1 for all values of x

In a city, 60% of the residents live in houses and 40% of the residents live in apartments. Of the people who live in houses, 35% own their own business. Of the people who live in apartments, 30% own their own business. If a person owns his or her own business, find the probability that he or she lives in a house. (Round your answer to two decimal places.)

.64

Click on the "A" in the left (orange) circle and drag until its probability is P(A) = 0.061. Click on the "B" in the right (blue) circle and drag until its probability is P(B) = 0.16. Place A entirely inside B. What is the value of P(A ∩ B)?

0.061

Leaving P(A) = 0.164 and P(B) = 0.07, move B until exactly half of its area intersects with A. Now what is the value of P(A ∪ B)?

0.199

Click on the "A" in the left (orange) circle and drag until its probability is P(A) = 0.164. Click on the "B" in the right (blue) circle and drag until its probability is P(B) = 0.07. Make sure the circles do not overlap. What is the value of P(A ∪ B)?

0.234

Of the last 100 customers entering a computer shop, 20 have purchased a computer. If the classical method for computing probability is used, find the probability that the next customer will purchase a computer.

0.50

If a penny is tossed seven times and comes up heads all seven times, what is the probability of heads on the eighth trial?

1/2

Leaving P(A) = 0.061 and P(B) = 0.16, move B until the value of P(A ∩ B) = 0.02. What fraction of A now intersects with B?

1/3

Consider the probability distribution below. x - f(x) 40 - 0.15 50 - 0.05 60 - 0.45 70 - 0.35 The expected value is 60. Find the variance of x.

100

The following represents the probability distribution for the daily demand of computers at a local store. 0 - 0.05 1 - 0.3 2 - 0.25 3 - 0.25 4 - 0.15 What is the expected daily demand?

2

Assume your favorite soccer team has 5 games left to finish the season. The outcome of each game can be win, lose or tie. What is the number of possible outcomes?

243

From a group of eight people, two individuals are to be selected at random. How many selections are possible?

28

The union of events A and B is the event containing all the sample points belonging to

A or B or both

Consider the bivariate distribution for the random variables x and y. The variance of the sum of x and y is

Greater than the sum of the variances by two times the covariance

Consider the bivariate distribution for the random variables x and y. The variance of a linear combination of x and y is

Var (ax + by) = a2 Var(x) + b2 Var(y) + 2ab σxy

The weight of an object is an example of

a continuous random variable

The number of customers that enter a store during one day is an example of

a discrete random variable

When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the _____ method.

classical

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the rule for

combinations

Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance

divided by the product of the standard deviations for x and y.

The use of the relative frequency method to develop discrete probability distributions leads to what is called a(n) _____ discrete distribution.

empirical

A weighted average of the values of a random variable, where the probability function provides weights, is known as the

expected value

Which of the following is a required condition for a discrete probability function?

f(x) ≥ 0 for all values of x

The intersection of two mutually exclusive events

must always be equal to 0

The multiplication law is potentially helpful when we are interested in computing the probability of

the intersection of two events

The collection of all possible sample points in an experiment is

the sample space

The addition law is potentially helpful when we are interested in computing the probability of

the union of 2 events