120 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 1 a. at most 6 of the calls involve a fax message? 2 b. exactly 6 of the calls involve a fax message? 3 c. at least 6 of the calls involve a fax message? 4 d. more than 6 of the calls involve a fax message? 5 e. the number of calls among the 25 that involve a fax transmission

a)0.5611

b)0.1828

c)0.6217

d)0.4389

e)6.25

Step-by-step explanation:

Let's define the following event :

X : ''Calls involving a fax message''

The random variable X can be modeled as a Binomial random variable.

N ~ Bi(n,p)

N ~ Bi(25,0.25)

Where n is the sample and p is the success probability

Let's also define nCr as the combinatorial number :

The probability function for X is :

Where k is the number of success

a)

b)

c)

d)

e) They are asking us about the expected value for random variable X

In a Binomial random variable :

E(X) = μ = n.p

the answer is d on edge

step-by-step explanation: