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 25 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 25 that involve a fax message?
f. What is the standard deviation of the number among the 25 calls that involve a fax message?
g. What is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations?

Question

07-07-2021
Mathematics

Answered

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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 25 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 25 that involve a fax message?
f. What is the standard deviation of the number among the 25 calls that involve a fax message?
g. What is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations?

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