When an opinion poll calls landline telephone numbers at random, approximately 4

Question

When an opinion poll calls landline telephone numbers at random, approximately 40% of the numbers are working residential phone numbers. The remainder are either non-residential, non-working, or computer/fax numbers. You watch the random dialing machine make 19 calls. (Round your answers to four decimal places.)

(a) What is the probability that exactly 3 calls reach working residential numbers?

(b) What is the probability that at most 3 calls reach working residential numbers?

(c) What is the probability that at least 3 calls reach working residential numbers?

(d) What is the probability that fewer than 3 calls reach working residential numbers?

(e) What is the probability that more than 3 calls reach working residential numbers?

Explanation / Answer

This is an instance of binomial probability. Use the following formula to comput ethe probabilities.

P(X=r)=nCr(p)^r(q)^n-r, where, p is probability of an event to occur, n is the total number of trials and r is the number of particular event to occur.

a. P(X=3)=19C3(0.40)^3(0.60)^16=0.0175

b. P(X less than equal to 3)=P(X=0)+P(X=1)+...+P(X=3)=0.0230

C. P(X greater than or equal to 3)=1-P(X < 3)=1-0.0054=0.9946

d. P(X <3)=P(X=0)+P(X=1)+P(X=2)=0.0054

e. P(X>3)=1-P(X less than equal to 3)=1-0.0230=0.97770

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