Homework SourseBusiness Majors Suppose 30 of business majors major in accou
Business Majors
Suppose 30% of business majors major in accounting. You take a random sample of 3 business majors.
Please show how the answer is worked.
1. {Business Majors Narrative} What is the chance that they all major in accounting?
2. {Business Majors Narrative} What is the chance that at least one majors in accounting?
3. {Business Majors Narrative} What is the chance that exactly one majors in accounting?
4. {Business Majors Narrative} What is the chance that none of them major in accounting?
Solution
1.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 3
p = the probability of a success = 0.3
x = the number of successes = 3
Thus, the probability is
P ( 3 ) = 0.027 [ANSWER]
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2.
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 3
p = the probability of a success = 0.3
x = our critical value of successes = 1
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 0 ) = 0.343
Thus, the probability of at least 1 successes is
P(at least 1 ) = 0.657 [ANSWER]
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3.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 3
p = the probability of a success = 0.3
x = the number of successes = 1
Thus, the probability is
P ( 1 ) = 0.441 [ANSWER]
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4.
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 3
p = the probability of a success = 0.3
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.343 [ANSWER]
