QUESTIONS
Question 1
If a seed is planted, it has a 80% chance of growing into a healthy plant.
If 9 seeds are planted, what is the probability that exactly 2 don’t grow?
Question 2
Using the Binomial distribution,
If n=9 and p=0.3,
find P(x=4)
Question 3
A poll is given, showing 25% are in favor of a new building project.
If 7 people are chosen at random, what is the probability that exactly 2 of them favor the new building project?
Question 4
A manufacturing machine has a 10% defect rate.
If 4 items are chosen at random, what is the probability that at least one will have a defect?
Question 5
About 1% of the population has a particular genetic mutation. 800 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 800.
Question 6
About 8% of the population has a particular genetic mutation. 900 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 900.
Question 7
When taking a 5 question multiple choice test, where each question has 3 possible answers, it would be unusual to get _______ or more questions correct by guessing alone.
Give your answer in the box above as a whole number.
Question 8
Multiple-choice questions each have 4 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.
Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC), where C denotes a correct answer and W denotes a wrong answer.
(round answer to 4 decimal places)
P(WWWWC) =
What is the probability of getting exactly one correct answer when 5 guesses are made?
(round answer to 4 decimal places)
P(exactly one correct answer) =
Question 9
Assume that a procedure yields a binomial distribution with a trial repeated n=19 times. Use either the binomial probability formula (or technology) to find the probability of k=7 successes given the probability p=0.51 of success on a single trial.
(Report answer accurate to 4 decimal places.)
P(X=k) =
Question 10
Assume that a procedure yields a binomial distribution with a trial repeated n=8 times. Use either the binomial probability formula (or technology) to find the probability of k=8 successes given the probability p=34% of success on a single trial.
(Report answer accurate to 4 decimal places.)
P(X=k) =
Question 11
Assume that a procedure yields a binomial distribution with a trial repeated n=11 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=8 successes given the probability p= 5/6 of success on a single trial.
(Report answer accurate to 4 decimal places.)
P(X=k) =
Question 12
Assume that a procedure yields a binomial distribution with a trial repeated n=14 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=14 successes given the probability q=0.34 of success on a single trial.
(Report answer accurate to 4 decimal places.)
P(X=k) =
Question 13
Assume that a procedure yields a binomial distribution with a trial repeated n=5 times. Use some form of technology to find the probability distribution given the probability p=0.158 of success on a single trial.
(Report answers accurate to 4 decimal places.)
| K | P(x = k) |
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
Question 14
Assume that a procedure yields a binomial distribution with a trial repeated n=5 times. Use some form of technology to find the cumulative probability distribution given the probability p=0.466 of success on a single trial.
(Report answers accurate to 4 decimal places.)
| K | P(x = k) |
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
Question 15
The television show Pretty Betty has been successful for many years. That show recently had a share of 22, which means, that among the TV sets in use, 22% were tuned to Pretty Betty. An advertiser wants to verify that 22% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Pretty Betty broadcast.
Find the probability that none of the households are tuned to Pretty Betty.
P(none) =
Find the probability that at least one household is tuned to Pretty Betty.
P(at least one) =
Find the probability that at most one household is tuned to Pretty Betty.
P(at most one) =
If at most one household is tuned to Pretty Betty, does it appear that the 22% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Pretty Betty unusual?)
- No, it is not wrong.
- Yes, it is wrong.
Question 16
A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 26 tablets, then accepts the whole batch if there is at most one that doesn’t meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 14% rate of defects?
(Report answer as a decimal value accurate to four decimal places.)
P(accept shipment) =
Question 17
A study was conducted to determine whether there were significant differences between college students admitted through special programs (such as retention incentive and guaranteed placement programs) and college students admitted through the regular admissions criteria. It was found that the graduation rate was 91% for the college students admitted through special programs.
If 10 of the students from the special programs are randomly selected, find the probability that at least 9 of them graduated.
prob =
If 10 of the students from the special programs are randomly selected, find the probability that exactly 7 of them graduated.
prob =
Would it be unusual to randomly select 10 students from the special programs and get exactly 7 that graduate?
- Yes, it is unusual
- No, it is not unusual
If 10 of the students from the special programs are randomly selected, find the probability that at most 7 of them graduated.
prob =
Would it be unusual to randomly select 10 students from the special programs and get at most 7 that graduate?
- No, it is not unusual
- Yes, it is unusual
Would it be unusual to randomly select 10 students from the special programs and get only 7 that graduate?
- Yes, it is unusual
- No, it is not unusual
Question 18
Air-USA has a policy of booking as many as 25 persons on an airplane that can seat only 23. (Past studies have revealed that only 87% of the booked passengers actually arrive for the flight.)
Find the probability that if Air-USA books 25 persons, not enough seats will be available.
prob =
Is this probability low enough so that overbooking is not a real concern for passengers if you define unusual as 5% or less?
- Yes, it is low enough not to be a concern
- No, it is not low enough to not be a concern
What about defining unusual as 10% or less?
- Yes, it is low enough not to be a concern
- No, it is not low enough to not be a concern.
Question 19
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.07.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company’s assumptions, calculate the probability that there are fewer than 4 tornadoes in a 13-year period.
Question 20
Mr. Caywood filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.57 probability of guessing any one game correctly.
What is the probability Mr. Caywood will pick all 32 of the first round games correctly?
What is the probability Mr. Caywood will pick exactly 8 games correctly in the first round?
What is the probability Mr. Caywood will pick exactly 19 games incorrectly in the first round?
Question 21
The Wilson family was one of the first to come to the U.S. They had 4 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson family had:
At least 3 girls?
At most 3 girls?
Question 22
A high school baseball player has a 0.162 batting average. In one game, he gets 6 at bats. What is the probability he will get at least 4 hits in the game?
Question 23
The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:
| Too Small | Too Large | Total | |
| Low Income | 17 | 23 | 40 |
| High Income | 27 | 8 | 35 |
| Total | 44 | 31 | 75 |
Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 3 decimal places. Give your to part d as a whole number.)
- The proportion of all children that drew the nickel too small is:
Assume that this proportion is true for ALL children (e.g. that this proportion applies to any group of children), and that the remainder of the questions in this section apply to selections from the population of ALL children.
- If 7 children are chosen, the probability that exactly 3 would draw the nickel too small is:
- If 7 children are chosen at random, the probability that at least one would draw the nickel too small is:
ANSWERS
If a seed is planted, it has a 80% chance of growing into a healthy plant.
If 9 seeds are planted, what is the probability that exactly 2 don’t grow?
Answer = 0.301989888
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