Please help with the following statistics question, There is some evidence to su
ID: 3377096 • Letter: P
Question
Please help with the following statistics question,
There is some evidence to suggest that businesses are moving out of states where unions are prevalent. In California, 18.4% of all workers belong to a union. Suppose 26 workers from California are selected at random. Demonstrate that X = the number of workers that belong to a union is a binomial random variable. Find the following probabilities: At most three California workers belong to a union. At least four but at most seven California workers belong to a union. Exactly eight California workers belong to a union. Less than twenty California workers do not belong to a union. More than nine but at most fourteen California workers do not belong to a union. What is the mean number of California workers that do belong to a union? Use the correct notation. What is the standard deviation for this probability distribution? Use the correct notation. Find P(mu - 2sigmaExplanation / Answer
a)
X is a binomial random variable as it only has two possible outcomes, that is, "belonging to a union" and "not belonging to a union". It also has a constant probability of success, 0.184.
Also, it seems here that the persons choose independently whether to join a union or not. Hence, X is a binomial random variable.
b)
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 26
p = the probability of a success = 0.184
x = the maximum number of successes = 3
Then the cumulative probability is
P(at most 3 ) = 0.269050207 [answer]
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c)
Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)
Here,
x1 = 4
x2 = 7
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 26
p = the probability of a success = 0.184
Then
P(at most 3 ) = 0.269050207
P(at most 7 ) = 0.910147397
Thus,
P(between x1 and x2) = 0.64109719 [answer]
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d)
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 = 26
p = the probability of a success = 0.184
x = the number of successes = 8
Thus, the probability is
P ( 8 ) = 0.052810822 [answer]
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