15 Abo selected at random and using a binomial distribution assumption. at 8% of
ID: 1122126 • Letter: 1
Question
15 Abo selected at random and using a binomial distribution assumption. at 8% of the production process produces defective parts. If five parts are 15a. What is the probability that 3 parts will be defective? 15b. What is the probability that at least 2 parts will be defective? 15c. What is the probability that more than 3 parts will be defective? 1Sd. What is the probability that less than 2 parts will be defective? 15e. What is the probability that at almost 2 part will be defective? 16 About 60 customers arrive in the store every two hours. In the half hour and assuming a Poisson Distribution 16a. What is the probability that 15 customers will arrive in the store? 16b. What is the probability that at least 10 customers will arrive in the store? lóc. What is the probability that more than 9 customers will arrive in the store? l6d. What is the probability less than 7 customers will arrive in the store? I6e. What is the probability that almost 5 customers will arrive in the store?Explanation / Answer
15.
P = .08
Q = 1- P = .92
n=5
As per the binomial distribution,
P(r) = nCr *(P)^r * Q^(n-r)
15.A
n= 5
P(r =3) = 5C3*(.08)^3 *.92^(2)
P(r=3) = 10*(.08)^3 *.92^(2) = .0043
15.B
Required probability = P(r =2) + P(r =3) + P(r =4) + P(r =5)
Required probability = 5C2*(.08)^2 *.92^3 + 5C3*(.08)^3 *.92^2 + 5C4*(.08)^4 *.92^1 + 5C5*(.08)^5 *.92^0
Required probability = 10*(.08)^2 *.92^3 + 10*(.08)^3 *.92^2 + 5*(.08)^4 *.92^1 + 1*(.08)^5 *.92^0
Required probability = .054
15.C
Required probability = P(r =4) + P(r =5)
Required probability = 5C4*(.08)^4 *.92^1 + 5C5*(.08)^5 *.92^0
Required probability = 5*(.08)^4 *.92^1 + 1*(.08)^5 *.92^0 = .000192
15.D
Required probability = P(r =0) + P(r =1)
Required probability = 5C0*(.08)^0 *.92^5 + 5C1*(.08)^1 *.92^4
Required probability = 1*(.08)^0 *.92^5 + 5*(.08)^1 *.92^4 = .945
15.E
Required probability = P(r =0) + P(r =1) + P(r =2)
Required probability = 5C0*(.08)^0 *.92^5 + 5C1*(.08)^1 *.92^4 + 5C2*(.08)^2 *.92^3
Required probability = 1*(.08)^0 *.92^5 + 5*(.08)^1 *.92^4 + 10*(.08)^2 *.92^3
Required probability = .9954
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