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 20% of the incoming calls involve fax messages and consider a sample of 20 incoming calls. a. What is the probability that i.exactly 3 of the calls involve a fax message? ii.at most 8 of the calls involve a fax message? b. Find the standard deviation and the expected number of calls among the 20 calls that involve a fax message? What is the probability that the number of calls among the 20 that involve a fax transmission exceeds the expected number by more than 2 standard deviations? Hint: find P (X > EX + 2o), where is standard deviation. c.

Explanation / Answer

Solution: n = 20 , p = 0.20

a.

i. P(X = 3) = 0.2054

ii. P(X < 8) = 0.9900

b. standard deviation = sqrt(20*0.20*0.80) = 1.7889

c. Ex = np = 20*0.20 = 4 , sd = 1.7889

P(X > EX + 2sigma) = P(X > 4 + 2*1.7889)

= P(X > 7.5778)

= 0.0228

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