Mathematics, 27.01.2021 20:30 chippedwood24

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 80% of the cases. Suppose the 13 cases reported today are representative of all complaints. Required:
a. How many of the problems would you expect to be resolved today? What is the standard deviation?
b. What is the probability 10 of the problems can be resolved today?
c. What is the probability 10 or 11 of the problems can be resolved today?
d. What is the probability more than 10 of the problems can be resolved today?

Answers: 1

Show answers

Answers

Answer from: veryrarecobain

a. 10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.

b. 0.2457 = 24.57% probability 10 of the problems can be resolved today

c. 0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today

d. 0.5017 = 50.17% probability more than 10 of the problems can be resolved today

Step-by-step explanation:

For each case, there are only two possible outcomes. Either they are solved, or they are not. Cases are independent of each other. 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.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

It can resolve customer problems the same day they are reported in 80% of the cases.

This means that p = 0.8

Sample of 13 cases:

This means that n = 13

a. How many of the problems would you expect to be resolved today? What is the standard deviation?

Expected:

E(X) = np = 13*0.8 = 10.4

Standard deviation:

$\sqrt{V(X)} = \sqrt{13*0.8*0.2} = 1.44$

10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.

b. What is the probability 10 of the problems can be resolved today?

This is P(X = 10) . So

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

$P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457$

0.2457 = 24.57% probability 10 of the problems can be resolved today.

c. What is the probability 10 or 11 of the problems can be resolved today?

This is p = P(X = 10) + P(X = 11) . So

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

$P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457$

$P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680$

p = P(X = 10) + P(X = 11) = 0.2457 + 0.2680 = 0.5137

0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today.

d. What is the probability more than 10 of the problems can be resolved today?

This is

P(X 10) = P(X = 11) + P(X = 12) + P(X = 13) . So

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

$P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680$

$P(X = 12) = C_{13,12}.(0.8)^{12}.(0.2)^{1} = 0.1787$

$P(X = 13) = C_{13,13}.(0.8)^{13}.(0.2)^{0} = 0.0550$

P(X 10) = P(X = 11) + P(X = 12) + P(X = 13) = 0.2680 + 0.1787 + 0.0550 = 0.5017

0.5017 = 50.17% probability more than 10 of the problems can be resolved today

Answer from: Quest

f is the midpoint of

Answer from: Quest

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41 $4.41/7 = $.63 each at fresh side

5 bagels for $3.60 $3.60/5 = $.72 each at value mart

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Martha needs 22.25 strawberries for every 5 smoothies she makes. complete the table to see how many strawberries she would need to make 10 smoothies and 20 smoothies.

Answers: 1

Answer

Mathematics, 21.06.2019 15:40

Given the following sampling distribution of one mean with a sample size 49, from a normally distributed population,find the population standard deviation, o.79828588912497

Answers: 3

Answer

Mathematics, 21.06.2019 16:30

Identify the converse of the following conditional: if a point is in the first quadrant, then its coordinates are positive. if the coordinates of a point are not positive, then the point is not in the first quadrant. if the coordinates of a point are positive, then the point is in the first quadrant. if a point is in the first quadrant, then its coordinates are positive. if a point is not in the first quadrant, then the coordinates of the point are not positive.

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Rena is building a 1: 180 scale model of a real castle. her model has a rectangular base that is 3 feet wide and 4 feet long what is the area of the base of the actual castle in square feet

Answers: 2

Answer

You know the right answer?

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown T...

Questions

Mathematics, 29.01.2020 03:59

1. population density is the number of people per unit of area. what is the population density of a state that has 1,627,260 people in 1,490 square mi...