Answer to Question #346962 in Statistics and Probability for Hlo

Question #346962

Question 2.8 [2, 3, 3]



Suppose that a telemarketer has a 12% chance of making a sale on any given call. If the



telemarketer makes average of 5 calls per hour, calculate:



a) The probability that the telemarketer will make exactly 2 sales during the shift.



b) The probability that the telemarketer will makes more than 4 sales during the shift.



c) What is the probability that the telemarketer makes more than 2 call during two hours?

1
Expert's answer
2022-06-06T06:22:08-0400

Let X=X= the number of sales: XBin(n,p)X\sim Bin(n, p)

a)

n=5,p=0.12,q=1p=0.88n=5, p=0.12, q=1-p=0.88



P(X=2)=(52)(0.12)2(0.88)52P(X=2)=\dbinom{5}{2}(0.12)^{2}(0.88)^{5-2}=0.098131968=0.098131968

b)

n=5,p=0.12,q=1p=0.88n=5, p=0.12, q=1-p=0.88



P(X>4)=P(X=5)=(55)(0.12)5(0.88)55P(X>4)=P(X=5)=\dbinom{5}{5}(0.12)^{5}(0.88)^{5-5}=0.0000248832=0.0000248832

c)

n=10,p=0.12,q=1p=0.88n=10, p=0.12, q=1-p=0.88



P(X>2)=1P(X=0)P(X=1)P(X>2)=1-P(X=0)-P(X=1)P(X=2)=1(100)(0.12)0(0.88)100-P(X=2)=1-\dbinom{10}{0}(0.12)^{0}(0.88)^{10-0}(101)(0.12)1(0.88)101(102)(0.12)2(0.88)102-\dbinom{10}{1}(0.12)^{1}(0.88)^{10-1}-\dbinom{10}{2}(0.12)^{2}(0.88)^{10-2}=0.10868179372=0.10868179372

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