Concept explainers
a.
Find the value of
a.
Answer to Problem 19P
The value of
Explanation of Solution
Calculation:
The binomial experiment with
The
Where, p is the probability of success.
Substitute
Thus, the probability of zero success is 0.3487.
b.
Find the value of
b.
Answer to Problem 19P
The value of
Explanation of Solution
Calculation:
Consider
The value of
Thus, the probability of two successes is 0.1937.
c.
Find the probability of at most two successes.
c.
Answer to Problem 19P
The probability of at most two successes is 0.9298.
Explanation of Solution
Calculation:
Here,
The probability
in the binomial probability formula. That is,
Substitute the other probability values from part (a) and (b),
Thus, the probability of at most two successes is 0.9298.
d.
Find the probability of at least one success.
d.
Answer to Problem 19P
The probability of at least one success is 0.6513.
Explanation of Solution
Calculation:
Here,
Substitute the value from part (a),
Thus, the probability of at least one success is 0.6513.
e.
Find the
e.
Answer to Problem 19P
The expected value of the binomial random variable is 1.
Explanation of Solution
Calculation:
The expected value of a binomial random variable is given by,
Substitute the values
Thus, the expected value of the binomial random variable is 1.
f.
Find the variance and standard deviation.
f.
Answer to Problem 19P
The variance of the binomial random variable is 0.9.
The standard deviation of the binomial random variable is 0.95.
Explanation of Solution
Calculation:
The variance of a binomial random variable is given by,
Substituting the values
The variance of the binomial random variable is 0.9.
The standard deviation of the random variable x is obtained by taking the square root of variance.
Thus, the standard deviation of the binomial random variable is given by,
The standard deviation of the binomial random variable is 0.95.
Want to see more full solutions like this?
Chapter 5 Solutions
Essentials of Business Analytics (MindTap Course List)
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardIf a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)arrow_forwardAssume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,