Based on labor statistics, 21% of workers in a particular profession are male. C
ID: 3129693 • Letter: B
Question
Based on labor statistics, 21% of workers in a particular profession are male. Complete parts a through e below based on a random sample of 8 workers in this profession. (round answers to four decimal places)
a. What is the probability that exactly one worker in the sample is male?
b. What is the probability that fewer than 4 workers in the sample are male?
c. What is the probability that more than 2 workers in the sample are male?
d. What are the mean and standard deviation for this distribution?
Explanation / Answer
a)
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 = 8
p = the probability of a success = 0.21
x = the number of successes = 1
Thus, the probability is
P ( 1 ) = 0.322625671 [ANSWER]
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b)
Note that P(fewer than x) = P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 8
p = the probability of a success = 0.21
x = our critical value of successes = 4
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 3 ) = 0.93408201
Which is also
P(fewer than 4 ) = 0.93408201 [ANSWER]
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c)
Note that P(more than x) = 1 - P(at most x).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 8
p = the probability of a success = 0.21
x = our critical value of successes = 2
Then the cumulative probability of P(at most x) from a table/technology is
P(at most 2 ) = 0.774500942
Thus, the probability of at least 3 successes is
P(more than 2 ) = 0.225499058 [ANSWER]
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d)
u = mean = np = 1.68 [ANSWER]
s = standard deviation = sqrt(np(1-p)) = 1.152041666 [ANSWER]
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