Chapter 4 and 5

statistical experiment

is a process that, when performed results in one and only one of many observations

sample point

an element of a sample space

event

includes one or more outcomes

simple event

includes one and only one outcome

compound event

at least two outcomes

The experiment of tossing a coin 4 times has

16 outcomes
2 x 2 x 2 x 2 = 16 or 24 = 16

A box contains a few red, a few black, and a few white marbles. Two marbles are randomly drawn from this box and the color of these marbles is observed. The total number of outcomes for this experiment is:

9
32 = 9
RRRBRW BBBRBW WWWRWB

You randomly select two households and observe whether or not they own a telephone answering machine.

Exactly one of them owns a telephone answering machine is a simple event.

You toss a coin nine times and observe 3 heads and 6 tails. This event is a

simple event

The probability of an event is always

between 0 and 1, inclusive

According to the relative frequency concept of probability, the probability of an event is

the number of times the given event is observed divided by the total number of repetitions of the experiment

conditional probability

is a probability
that an event will occur given that another event has already occurred

marginal (simple) probability

probability of an event without considering any other event

Two mutually exclusive events____?

cannot occur together

Two events are independent if the occurrence of one event
does not affect the probability of the occurrence of the other event

Two events are independent if the occurrence of one event
does not affect the probability of the occurrence of the other event

Two complementary events

taken together include all outcomes for an experiment

Two events A and B are independent if

P(A|B) is equal to P(A)

If PA B P(A)P(B), then events A and B are

independent

random variable

a variable whose value is determined by the outcome of a random experiment

discrete random variable

a random variable: whose set of values is countable

continuous random variable

a random variable that can assume any value in one or more intervals

probability distribution table of a discrete random variable

all of the values that the random variable can assume and their corresponding probabilities

mean of a discrete random variable

the mean of its probability distribution

mean of a discrete random variable

is its expected value

The formula used to obtain the mean of a discrete random variable is

zxP(x)

The standard deviation of a discrete random variable is

the standard deviation of its probability distribution

n! "n factorial" represents

the product of all integers from n to 1

The factorial of zero

is 1

The number of combinations for selecting zero elements from 8 distinct elements is

is 1

The number of combinations for selecting 14 elements from 14 distinct elements is

is 1

A court randomly selects a jury of 7 persons from a group of 16 persons. The total number of combinations is

11440

Condition of a binomial experiment:

1) There are n identical trials
2) Each trial has two and only two outcomes
3) p is the probability of success, q is the probability of failure, and p + q = 1
4) The trials are independent

binomial experiments, the outcome called a "success" is

an outcome to which the question refers

parameters of the binomial probability distribution are

n and p

binomial probability distribution is symmetric if

p is equal to .50

binomial probability distribution is right-skewed if

p is less than .50

The binomial probability distribution is left-skewed if

p is greater than .50

The mean of a binomial distribution is equal to:

np

The standard deviation of a binomial distribution is equal to

square root of npq

Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 13 such college graduates hired recently by companies, exactly 5 wil

P(5) = 0.0022

The joint probability of two independent events A and B is the Multiplication Rule for Independent Events

P(A and B) = P(A)P(B)

The joint probability of two mutually exclusive events is always equal to

0.00

The probability that a person is a college graduate is 0.34 and that he/she has high blood pressure is 0.15. Assuming that these two events are independent, the probability that a person selected at random is a college graduate and has high blood pressure

P(G and H) = 0.34 x 0.15 = 0.051

The union of two events A and B represents the outcomes that are

either in A or in B or in both A and B