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Answer:
A.)
0.852 ; 0.999 ; 0.013
B.)
0.018 ; 0.593 ; 0.050
Step-by-step explanation:
Given :
Proportion of marketing personnel that are extrovert, p = 0.75
1 - p = 1 - 0.75 = 0.25
Proportion of computer programmers that are introverts, p = 0.55
1 - p = 1 - 0.55 = 0.45
According to binomial distribution formula :
P(x =x) = nCx * p^x * (1 - p)^(n - r)
A.) n = 15
Probability that 10 or more are extrovert
P(x ≥ 10) = p(x = 10) + p(x = 11) +... p(x = 15)
To save computation time, we can use a binomial probability calculator ;
P(x ≥ 10) = 0.8516 = 0.852
Probability that 5 or more are extrovert :
P(x ≥ 5) = p(x = 5) + p(x = 6) +... p(x = 15)
To save computation time, we can use a binomial probability calculator ;
P(x ≥ 5) = 0.9999 = 0.999
Probability that all are extrovert :
P(x = 15) = 15C15 * 0.75^15 * 0.25^0
P(x = 15) = 1 * 0.75^15 * 0.25^0
P(x = 15) = 0.01336 = 0.013
B.
What is the probability that all are introverts?
n = 5
None are introvert :
P(x = 0) = 5C0 * 0.55^0 * 0.45^5
P(x = 0) = 1 * 1 * 0.0184528125
P(x = 0) = 0.01845 = 0.018
P(x ≥ 3) = p(3) + p(4) + p(5)
To save computation time, we can use a binomial probability calculator ;
P(x ≥ 3) = 0.5931 = 0.593
Probability that all are introvert
P(x = 5) = 5C5 * 0.55^5 * 0.45^0
P(x = 5) = 1 * 0.55^5 * 0.45^0
P(x = 5) = 0.0503 = 0.050