A particular telephone number is used to receive both voice calls and fax messag

Question

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 12 incoming calls. What is the probability that a. At most 6 of the calls involve a fax message? b. Exactly 6 of the calls involve a fax message? c. At least 6 of the calls involve a fax message? d. More than 6 of the calls involve a fax message? e. What is the expected number of calls among the 12 that involve a fax message? f. What is the standard deviation of the number among the 12 calls that involve a fax message? g. What is the probability that the number of calls among the 12 that involve a fax transmission exceeds the expected number by more than 2 standard deviations?

Explanation / Answer

This is binomial distribtuion with n=12 and p=0.25, as events are independent, p is same for all, two outcomes and n is constant

We know P(x)=ncx*p^x*(1-p)^(n-x)

a. P(x<=6)=0.9857

b. P(x=6)=0.0401

c. P(x>=6)=0.0544

d. P(x>6)=0.0143

e. Mean=np=0.25*12=3

f. Standard deviation=sqrt(npq)=sqrt(12*0.25*0.75)=1.5

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