1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vlad1618 [11]
3 years ago
7

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

dent. (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). (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). (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.
Mathematics
1 answer:
aev [14]3 years ago
7 0

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.

You might be interested in
Which equation represents an inverse variation?
Sphinxa [80]

Answer: Choice C) y = 30/x

Inverse variation equations are of the form y = k/x. In this case, k = 30. We can rearrange the format to get x*y = k after multiplying both sides by x. So y = 30/x can be turned into x*y = 30.

7 0
3 years ago
What is the transformation of the graph from its parent function​
VLD [36.1K]

Answer:

The transformation is left 1 hope it is right

Step-by-step explanation:

7 0
2 years ago
The aquarium charges an entrance fee of $5 per child and $12 per adult. On one day, 100 people visited the aquarium. They collec
igor_vitrenko [27]

Answer:

We set up 2 equations

A) C + A = 100

B) 5C + 12A = 780

We multiply A by -5

A) -5C -5A = -500   then we add B

B) 5C + 12A = 780

7A = 280

Number of Adults = 40

5C = 780 - 40*12

5C = 780 -480

5C = 300

Number of Children = 60

Step-by-step explanation:

6 0
3 years ago
In a lab experiment, 1900 bacteria are placed in a petri dish. The conditions are such
GREYUIT [131]

Answer:

393 bacteria

Step-by-step explanation:

First find how much it would increase per hours :

1900 / 29 = 65.5172414

Then take this and multiply it by 6 to get :

393.103448

Round it to the nearest whole number to get:

393 bacteria

3 0
3 years ago
HELLLLLLLLPPPPPPPPPPPP!!!!!!
ICE Princess25 [194]

Answer:

3 bars of soap and 2 toothbrushes.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • A bag contains four red marble, five blue marbles, and two green marbles. if one marble is chosen randomly, what is the probabil
    13·2 answers
  • What is the unit rate to the nearest cent per ounce if there is size is pint and the quantity is 16oz and the price is $3.98
    5·1 answer
  • a bag contains 5 red 3 green 4 blue and 8 yellow marbles find the probability of randomly selecting a green marble and then a ye
    11·1 answer
  • Identify an equation in point-slope form for the line perpendicular to y = 3x + 5
    8·1 answer
  • Is 5 a solution to -3x=15
    6·2 answers
  • 5. What is the Standard deviation for the following set<br> of data?<br> 6,4,9, 5, 5, 4,5
    13·1 answer
  • Please help with question 7 and 8 also 9
    14·1 answer
  • HELP DUE AT 8: 30 ASAP!
    10·1 answer
  • Please help it urgent!!!!
    8·1 answer
  • Patricia is making two sizes of hamburgers: 0.5-pound andd 0.25-pound. How many of each size of hamburger could she make with 3.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!