Math 136 - Introduction to Statistics » Fall 2021 » Homework 5 Binomial Distribution

Need help with your exam preparation?

Question #1
Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 19 times, keeping track of the numbers that are rolled
A.   Not binomial: the trials are not independent.
B.   Procedure results in a binomial distribution.
C.   Not binomial: there are more than two outcomes for each trial.
D.   Not binomial: there are too many trials.
Question #2
Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Rolling a single die 46 times, keeping track of the "fives" rolled
A.   Procedure results in a binomial distribution.
B.   Not binomial: the trials are not independent
C.   Not binomial: there are more than two outcomes for each trial.
D.   Not binomial: there are too many trials.
Question #3
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n = 4, x = 3, p =  1/6
A.   0.0116
B.   0.0231
C.   0.0039
D.   0.0154
Question #4
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n = 10, x = 2, p = 1/3
A.   0.2156
B.   0.0028
C.   0.1951
D.   0.1929
Question #5
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n = 30, x = 12, p = 0.20
A.   0.0064
B.   0.0139
C.   0.1082
D.   0.0028
Question #6
A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?
A.   0.172
B.   0.117
C.   0.055
D.   0.945
Question #7
In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?
A.   0.9815
B.   0.9846
C.   0.0547
D.   0.913
Question #8
In a study, 39% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health.
A.   0.1256
B.   0.0667
C.   0.121
D.   0.1877
Question #9
The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 11 participants there have been only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer women when 11 people are picked?
A.   0.0322
B.   0.0327
C.   0.0059
D.   0.0269
Question #10
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 33; p = .2
A.   μ = 6.9
B.   μ = 7.3
C.   μ = 6.6
D.   μ = 6.1
Question #11
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 20; p = 3/5
A.   μ = 11.5
B.   μ = 12.3
C.   μ = 12.7
D.   μ = 12.0
Question #12
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 25; p = 3/5
A.   σ = 6.57
B.   σ = 2.45
C.   σ = 0.04
D.   σ = 5.72
Question #13
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 2661; p = .63
A.   σ = 29.03
B.   σ = 24.91
C.   σ = 22.50
D.   σ = 28.18
Question #14
Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than μ - 2σ or greater than μ + 2σ. A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 687 consumers who recognize the Dull Computer Company name?
A.   Yes
B.   No
Question #15
Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than μ - 2σ or greater than μ + 2σ. A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 687 consumers who recognize the Dull Computer Company name?
A.   Yes
B.   No

Need help with your exam preparation?