<img src="https://tex.z-dn.net/?f=15%20%2B%2015%20%2B%2030" id="TexFormula1" title="15 + 15 + 30" alt="15 + 15 + 30" align="absm

The probability that your call to a service line is answered in less than 30 seconds is 0.85. Assume that your calls are indepen

aev [14]

Answer:

a) 0.1720

b) 0.8298

c) 19

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.85$

(a) If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ .

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.85)^{9}.(0.15)^{3} = 0.1720$

(b) If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.85)^{16}.(0.15)^{4} = 0.1821$

$P(X = 17) = C_{20,17}.(0.85)^{17}.(0.15)^{3} = 0.2428$

$P(X = 18) = C_{20,18}.(0.85)^{18}.(0.15)^{2} = 0.2293$

$P(X = 19) = C_{20,19}.(0.85)^{19}.(0.15)^{1} = 0.1368$

$P(X = 20) = C_{20,20}.(0.85)^{20}.(0.15)^{0} = 0.0388$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1821 + 0.2428 + 0.2293 + 0.1368 + 0.0388 = 0.8298$

(c) If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.85 = 18.7$

The nearest integer to 18.7 is 19.

7 0

3 years ago

Geometry math question no Guessing and Please show work thank you

ANTONII [103]

Line DQ is equal to 7. Since point Q is the centeriod, this means that line DQ will equal the same as line QD. Thus, line QD is 7 making like DQ 7 as well. Hope that helped :))

7 0

3 years ago

What is an equation in point slope form of the line that passes through the point (6,-2) and had a slope of 3

ch4aika [34]

Answer:

y - 6 = 3(x + 2)

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

Given: m(slope) = 3, (6, -2)

(x1, y1) = (6, -2)

Input the given values of the slope and the point into the equation for point-slope form:

y - (-2) = 3(x - 6)

y + 2 = 3(x - 6)

The equation written in point-slope form is: y + 2 = 3(x - 6)

7 0

3 years ago

Ricardo is factoring the polynomial, which has four terms. 5x3 20x2 2x 8 5x2(x 4) 2(x 4) Which is the completely factored form o

umka21 [38]

The factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).

<h2>Polynomial</h2>

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.