Question

0/2 points Previous Answers DEVORESTATS 3.E.051. My Notes Ask Your Teacher 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 20 incoming calls. (a) What is the expected number of calls among the 20 that involve a fax message? E(X) = (b) What is the standard deviation of the number among the 20 calls that involve a fax message? (Round your answer to three decimal places.) Oy = (c) 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? (Round your answer to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Talk to a Tutor

Answer 1

X: Number of calls that involve a fax transmission has a binomial distribution with n = 20 and p = 0.25

(a) Expected number of calls among 20 that involve a fax message.

E(X) = n * p = 20 * 0.25 = 5

E(X) = 5

(b) Standard deviation.

Ox= n*p*(1 - p) = 20 * 0.25*(1 -0.25) = 1.936

0x = 1.936

(c) P(number of calls among 20 that involve a fax message exceeds the expected value by more than 2 standard deviations)

that is

P(X > E(X) +2* ox) = P(X > 5 + 2 * 1.936) = P(X > 8.872) = P(X >9)

Using binomial distribution table or excel the probability is,

P(X > 9) = 1 - P(X <=9)

Using excel, the probability P(X< = 9) is,

=binomdist(x, n, p, cumulative) = binomdist(9,20,0.25,1) = 0.986

P(X > 9) = 1 - 0.986 = 0.014

The probability that the number of calls exceeds the expected value by more than 2 standard deviation is 0.014