ECO 251: SOPHIA-INTRODUCTION TO STATISTICS UNI
3-MILESTONE
27 questions were answered correctly.
1
John makes random guesses on his multiple-choice test, which has five
options for each question. Let the random variable X be the number of
guesses taken before guessing correctly.
Assuming the guesses are independent, find the probability that he
doesn't guess correctly until his 6th guess.
•
0.0789
•
0.0655
•
0.3277
•
0.3521
RATIONALE
Since we are looking for the probability until the first success, we will use
the following Geometric distribution formula:
The variable k is the number of trials until the first success, which in this
case, is 6 guesses.
The variable p is the probability of success, which in this case, a success is
considered getting a question right on a multiple-choice test with five
options, which would be 1/5 or 0.2.
CONCEPT
,ECO 251: SOPHIA-INTRODUCTION TO STATISTICS UNI
3-MILESTONE
Geometric Distribution
2
Which of the following is a condition of binomial probability
distributions?
•
All observations are mutually exclusive.
•
,ECO 251: SOPHIA-INTRODUCTION TO STATISTICS UNI
3-MILESTONE
All observations made are dependent on each other.
•
All observations made are independent of each other.
•
All observations are made randomly.
RATIONALE
In the binomial distribution we always assume independence of trials. This
is why we simply multiply the probability of successes and failures directly
to find the overall probability.
CONCEPT
Binomial Distribution
3
A survey asked 1,000 people which magazine they preferred, given three
choices. The table below breaks the votes down by magazine and age
Age Below 40 Age 40 an
group.
The National Journal 104 20
Newsday 120 23
The Month 240 10
If a survey is selected at random, what is the probability that the
person voted for "Newsday" and is also age 40 or older? Answer
choices are rounded to the hundredths place.
•
0.23
•
0.66
•
0.54
, ECO 251: SOPHIA-INTRODUCTION TO STATISTICS UNI
3-MILESTONE
•
0.34
RATIONALE
If we want the probability of people who voted for "Newsday" and are also
age 40 and over, we just need to look at the box that is associated with both
categories, or 230. To calculate the probability, we can use the following
formula:
3-MILESTONE
27 questions were answered correctly.
1
John makes random guesses on his multiple-choice test, which has five
options for each question. Let the random variable X be the number of
guesses taken before guessing correctly.
Assuming the guesses are independent, find the probability that he
doesn't guess correctly until his 6th guess.
•
0.0789
•
0.0655
•
0.3277
•
0.3521
RATIONALE
Since we are looking for the probability until the first success, we will use
the following Geometric distribution formula:
The variable k is the number of trials until the first success, which in this
case, is 6 guesses.
The variable p is the probability of success, which in this case, a success is
considered getting a question right on a multiple-choice test with five
options, which would be 1/5 or 0.2.
CONCEPT
,ECO 251: SOPHIA-INTRODUCTION TO STATISTICS UNI
3-MILESTONE
Geometric Distribution
2
Which of the following is a condition of binomial probability
distributions?
•
All observations are mutually exclusive.
•
,ECO 251: SOPHIA-INTRODUCTION TO STATISTICS UNI
3-MILESTONE
All observations made are dependent on each other.
•
All observations made are independent of each other.
•
All observations are made randomly.
RATIONALE
In the binomial distribution we always assume independence of trials. This
is why we simply multiply the probability of successes and failures directly
to find the overall probability.
CONCEPT
Binomial Distribution
3
A survey asked 1,000 people which magazine they preferred, given three
choices. The table below breaks the votes down by magazine and age
Age Below 40 Age 40 an
group.
The National Journal 104 20
Newsday 120 23
The Month 240 10
If a survey is selected at random, what is the probability that the
person voted for "Newsday" and is also age 40 or older? Answer
choices are rounded to the hundredths place.
•
0.23
•
0.66
•
0.54
, ECO 251: SOPHIA-INTRODUCTION TO STATISTICS UNI
3-MILESTONE
•
0.34
RATIONALE
If we want the probability of people who voted for "Newsday" and are also
age 40 and over, we just need to look at the box that is associated with both
categories, or 230. To calculate the probability, we can use the following
formula:
