Suppose approximately 75% of all marketing personnel are extroverts, whereas abo
ID: 3045538 • Letter: S
Question
Suppose approximately 75% of all marketing personnel are extroverts, whereas about 50% of all computer programmers are introverts (Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probablity that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the probability that all are extroverts? (b) In a group of 5 computer programmers, what is the probability that none are introverts? What is the probability that 3 or more are introverts? What is the probability that all are introverts?Explanation / Answer
(a)
At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?
Solution:
We are given
n = 15, p = 0.75
We have to find P(X10)
P(X10) = P(X=10) + P(X=11) + P(X=12) + P(X=13) + P(X=14) + P(X=15)
P(X=x) = nCx*p^x*(1 – p)^(n – x)
P(X=10) = 15C10*0.75^10*0.25^5 = 0.165146
P(X=11) = 15C11*0.75^11*0.25^4 = 0.225199
P(X=12) = 15C12*0.75^12*0.25^3 = 0.225199
P(X=13) = 15C13*0.75^13*0.25^2 = 0.155907
P(X=14) = 15C14*0.75^14*0.25^1 = 0.066817
P(X=15) = 15C15*0.75^15*0.25^0 = 0.013363
P(X10) = 0.851632
Required probability = 0.852
What is the probability that 5 or more are extroverts?
We are given
n = 15, p = 0.75
We have to find P(X5)
P(X5) = 1 – P(X4)
P(X5) = 1 - 0.000115
P(X5) = 0.999885
Required probability = 1.000
What is the probability that all are extroverts?
We are given
n = 15, p = 0.75
We have to find P(X=15)
P(X=x) = nCx*p^x*(1 – p)^(n – x)
P(X=15) = 15C15*0.75^15*0.25^0 = 0.013363
Required probability = 0.013
(b)
In a group of 5 computer programmers, what is the probability that none are introverts?
We are given n = 5, p = 0.5
We have to find P(X=0)
P(X=x) = nCx*p^x*(1 – p)^(n – x)
P(X=0) = 5C0*0.5^0*0.5^5 = 0.03125
Required probability =0.031
What is the probability that 3 or more are introverts?
We are given n = 5, p = 0.5
We have to find P(X 3)
P(X 3) = 1 – P(X2) = 1 – 0.5
P(X 3) = 0.5
Required probability = 0.500
What is the probability that all are introverts?
We are given n = 5, p = 0.5
We have to find P(X = 5)
P(X=x) = nCx*p^x*(1 – p)^(n – x)
P(X=5) = 5C5*0.5^5*0.5^0 = 0.03125
Required probability = 0.031
(Probabilities are calculated by using Binomial table or excel.)