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 correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.