Answer:
- a. The expected number of calls among the 25 that involve a fax message is 6.25.
- b. The standard deviation of the number among the 25 calls that involve a fax message is approximately 2.167.
Explanation:
(a) To find the expected number of calls among the 25 that involve a fax message, we can use the formula for the expected value of a random variable.
Given that 25% of the incoming calls involve a fax message, we can determine the expected number of fax message calls as follows:
E(X) = n * p
where E(X) is the expected value, n is the number of trials, and p is the probability of success.
In this case, the number of trials is 25 and the probability of success (i.e., the probability that an incoming call involves a fax message) is 25% or 0.25.
Therefore, the expected number of calls among the 25 that involve a fax message is:
E(X) = 25 * 0.25 = 6.25
Therefore, the expected number of calls among the 25 that involve a fax message is 6.25.
(b) To find the standard deviation of the number among the 25 calls that involve a fax message, we can use the formula for the standard deviation of a binomial distribution.
The formula for the standard deviation of a binomial distribution is given by:
σ = √(n * p * (1 - p))
where σ is the standard deviation, n is the number of trials, and p is the probability of success.
In this case, the number of trials is 25 and the probability of success (i.e., the probability that an incoming call involves a fax message) is 25% or 0.25.
Therefore, the standard deviation of the number among the 25 calls that involve a fax message is:
σ = √(25 * 0.25 * (1 - 0.25)) = √(25 * 0.25 * 0.75) = √(4.6875) = 2.167
Therefore, the standard deviation of the number among the 25 calls that involve a fax message is approximately 2.167.
Your question is incomplete, but most probably the full question was:
A particular telephone number is used to receive both voice calls and fax message. Suppose that 25% of the incoming calss involve fax message, and consider a sample of 25 incoming calls
(a) What is the expected number of calls anong the 25 that involve a tax message?
E(X)=____
(b) What is the standard deviation of the number among the 25 calls that involve of fax message?
dx=_____