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)-5

(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.) Ox= 1.936

(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.)

Step-by-step explanation:

let us suppose that each call out of the 20 is indepent from each other. We have that the probability of having a fax message is 0.25. Let X the number of calls among the 20 that involve a fax message.

Then, the random variable X is distributed as a binomial random variable.

Recall the following for binomial random variables

and that the standar deviation is the square root of the variance. Then,

a)

b)

c) We want

We have that

Then, the desired probabilty is 0.041.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.