The fraction: 340

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

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:

$p = 0.75$

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

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

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

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

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

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

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

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

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Juanita runs every third day and swims every fifth day. If Juanita runs and swims today, in how many days will she run and swim

Ber [7]

we know that

The least
common multiple (LCM) of two or more numbers is the least

number, other than zero, that is a multiple of all the numbers.

In this problem, we are looking for the least common multiple of $3$ and $5$

So

Multiply $3$ by $5$

$LCM=3*5\\ LCM=15$

therefore

On the $15th$ day after today, she will do both on the same day

the answer is

$15 days$

3 0

3 years ago

Read 2 more answers

What’s the solution to the system 5y=6x-4 and 3y=-6x+20

Elina [12.6K]

Answer:

6x-5y=4

6x+3y=30

Step-by-step explanation:

Move variable to the left

5y=6x-4

Reorder the terms

5y-6x=-4

Change the signs

-6x+5y=-4

Move variable to the left

3y=-6x+20

Reorder the terms

3y+6x=20

3 0

3 years ago

In the United States, a person eats more than 40,000 pounds of bread in a lifetime if she or he lives to be 80 years old. Does t

Shalnov [3]

Look at some shorter periods of time to decide whether their reasonable. Do that by simplifying the fraction. . . . . 40,000 pounds / 80 years = 4,000 pounds / 8 years = 2,000 pounds (1 ton) / 4 years = 1,000 pounds / 2 years (have you decided yet ? Well, simplify it some more) 1,000 pounds / 2 years = 500 pounds per year = almost 1 and 1/2 pounds of bread every day of your life. NOW what do you think ? Make sense ?

8 0

3 years ago

Find the measure of angle A.

polet [3.4K]

The measure of angle A is 80

8 0

3 years ago

The fraction: 340 | 3/4