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
Find the solution of y = 3x + 3 for x = –3.
mixas84 [53]

Answer:

<h2>(-3,-6)</h2>

Step-by-step explanation:

hope it help you

plz follow me

3 0
3 years ago
Read 2 more answers
Question 10
Anna [14]

Answer:

Step-by-step explanation:

5 0
3 years ago
Which is the equivalent decimal form of 4 1/7
Gwar [14]
First, make it an improper fraction, 7x4 is 28. 28+1 is 29. So the improper fraction is 29/7. Then, divide 29 by 7. The answer is 4.14 rounded to the tenths place.
8 0
3 years ago
Jacks basketball team went to the movies. Adults were $12.00. 5 adults and 12 players came. The total was $120. What was the cos
avanturin [10]
5 dollars is the answer
5 0
2 years ago
Read 2 more answers
A wheel has a diameter of 21 inches. About how far does it travel if it makes 30 complete revolutions?
Lelu [443]
3 multiplied by 20 is 60

Multiply this by 10 and you get 600

1 Multiplied by 30 is 30

Find the total of the two answers (Which is 630) this is your answers
4 0
3 years ago
Other questions:
  • Solve the inequality. -x/2 is less than or equal to 1. a. x ≤ –2 b. x ≤ 3 c. x ≥ 2 d. x ≥ –2
    5·2 answers
  • The term that describes how long it takes a function to repeat its behavior is the
    15·2 answers
  • Rewrite the expression 4×12 two different ways to show the distributive property over both addition and subtraction
    11·1 answer
  • Someone help please ://////
    14·1 answer
  • The mean of data set A is 43.5 and the MAD is 3.7. The mean of data set B is 12.8 and the MAD is 4.1.
    11·2 answers
  • What is the circumference of a circle with a diameter of 8 feet? Use 3.14 for<br> TT.<br> d = 8 ft
    7·2 answers
  • HELP ASAP!!!
    6·1 answer
  • PWEASE HELP MWEEEEE UwU
    9·1 answer
  • Find the value.plzzz I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz​
    8·1 answer
  • Pls answer this!! someone!!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!