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Section 6.2 Homework
Section 6.2 Homework
1. What are the four requirements for a probability experiment to be a binomial experiment? Choose from the list below.
- Each trial has more than two outcomes
- There is an unlimited number of trials.
- There is a fixed number of trials.
- The probability of a success remains the same in each case.
- The probability of a success does not remain the same in each case.
- The outcomes are dependent on each other.
- There are two trials.
- Each trial has only two outcomes.
- The outcomes are independent of each other.
2. Determine whether the random variable X has a binomial distribution. If it does, state the number of trials n. If it does not, explain why not.
A coin is flipped until a Head appears. Let X be the number of Heads.
The random variable ________ a binomial distribution.
Choose a statement that explains why X does not have a binomial distribution.
- The number of trials is not fixed.
- There are more than two possible outcomes for each trial.
- The probability of success is not the same for each trial.
- The trials are not independent.
- does not represent the number of successes that occur.
3. A binomial experiment has the given number of trials n and the given success probability p.
n=6, p=0.6
(a)Determine the probability P(3). Round the answer to at least four decimal places.
P(3) =
(b)Find the mean. Round the answer to two decimal places.
The mean is ______.
(c)Find the variance and standard deviation. Round the variance to two decimal places and standard deviation to at least three decimal places.
The variance is ____
The standard deviation is ____
4. A binomial experiment has the given number of trials n and the given success probability p.
n = 13, p = 0.2
(a) Determine the probability P (Fewer than 2). Round the answer to at least four decimal places.
P (Fewer than 2) =
(b)Find the mean. Round the answer to two decimal places.
The mean is _____.
(c)Find the variance and standard deviation. Round the variance to two decimal places and standard deviation to at least three decimal places.
The variance is
The standard deviation is
5. Match each TI-84 PLUS calculator command with the probability being calculated.
(a) 1 – binomcdf (n, p, 5) _______________
(b)binompdf (n, p, 5) __________________
(c)binomcdf (n, p, 5) – binompdf (n, p, 0) ________________.
(d)binomcdf (n, p, 5) _________________________
6. Your flight has been delayed: At Denver International Airport, 83% of recent flights have arrived on time. A sample of 14 flights is studied. Round the probabilities to at least four decimal places.
(a) Find the probability that all 14 of the flights were on time.
The probability that all 14 of the flights were on time is ____
(b) Find the probability that exactly 12 of the flights were on time.
The probability that exactly 12 of the flights were on time is _______
(c) Find the probability that 12 or more of the flights were on time.
The probability that 12 or moe or more of the flights were on time is _______
(d) Using a cutoff of 0.05, would it be unusual for 13 or more of the flights to be on time?
It ___ be unusual for 13 or more of the flights to be on time since the probability is ______
7. Google it: According to a recent report, 67% of internet searches in a particular month used the Google search engine. Assume that a sample of 20 searches is studied. Round the answers to at least four decimal places.
(a) What is the probability that three or more of them have type O negative blood?
The probability that three or more of them have type O negative blood is ______.
(b) What is the probability that fewer than five of them have type O negative blood?
The probability that fewer than five of them have type O negative blood is ________
(c) Using a cutoff of 0.05 would it be unusual if none of the donors had type O negative blood?
It ____ be unusual if none of the donors had type O negative blood since the probability is ________
9. Blood types: The blood type O negative is called the “universal donor” type, because it is the only blood type that may safely be transfused into any person. Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type O negative blood. For this reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S. residents have type O negative blood. Assume that a blood bank has recruited 21 donors.
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