Please help. 21 points

work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company deci

NISA [10]

Answer:

Step-by-step explanation:

Here is the complete question.

Dominique, Marco, Roberto , and John work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to attend will have their names drawn from a hat. This is like obtaining a simple random sample of size 2. (a) Determine the sample space of the experiment. That is, list all possible simple random samples of size n = 2. (b) What is the probability that Dominique and Marco attend the conference? (c) What is the probability that John attends the conference? (d) What is the probability that John stays home?

Since there are four employees to select the two to send from. then for us to get the sample space for the experiment we need to merge all possible two employees and represent them as set.

Let D = Dominique, M = Marco, R = Roberto and J = John

a) The sample space for the experiment is the total number of possible outcomes that we can have. It is as given below

S = 4C2 = 4!/(4-2)!2! (Selecting 2 out of 4 employees)

Total sample space = 4!/2!2!

Total sample space = 4*3*2!/2!2

Total sample space = 12/2 = 6

The sample space are S = {DM, DR, DJ, MR, MJ, RJ}

b) Probability is the ratio of number of event to the sample space.

P = n(E)/n(S)

Given n(S) = 6

n(E) is the event of Dominique and Marco attending the conference.

E = {DM}

n(E) = 1

P(D and M) = 1/6

Hence the probability that Dominique and Marco attend the conference is 1/6

c) For John to attend the conference, the event outcome will be given as;

E = {DJ, MJ, RJ}

n(E) = 3

n(S) = 6

Probability for John to attend the conference is 3/6 = 1/2

d) Probability that John stays at home = 1 - Prob (John attends the conference)

Probability that John stays at home = 1 - 1/2

Probability that John stays at home = 1/2

7 0

3 years ago

The Resource Conservation and Recovery Act mandates the tracking and disposal of hazardous waste produced at U.S. facilities. Pr

aniked [119]

Answer:

(a) $E(X) = 0.383$

The expected number in the sample that treats hazardous waste on-site is 0.383.

(b) $P(x = 4) = 0.000169$

There is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

Step-by-step explanation:

Professional Geographer (Feb. 2000) reported the hazardous waste generation and disposal characteristics of 209 facilities.

N = 209

Only eight of these facilities treated hazardous waste on-site.

r = 8

a. In a random sample of 10 of the 209 facilities, what is the expected number in the sample that treats hazardous waste on-site?

n = 10

The expected number in the sample that treats hazardous waste on-site is given by

$E(X) = \frac{n \times r}{N}$

$E(X) = \frac{10 \times 8}{209}$

$E(X) = \frac{80}{209}$

$E(X) = 0.383$

Therefore, the expected number in the sample that treats hazardous waste on-site is 0.383.

b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site

The probability is given by

$P(x = 4) = \frac{\binom{r}{x} \binom{N - r}{n - x}}{\binom{N}{n}}$

For the given case, we have

N = 209

n = 10

r = 8

x = 4

$P(x = 4) = \frac{\binom{8}{4} \binom{209 - 8}{10 - 4}}{\binom{209}{10}}$

$P(x = 4) = \frac{\binom{8}{4} \binom{201}{6}}{\binom{209}{10}}$

$$ P(x = 4) = \frac{70 \times 84944276340}{35216131179263320}$

$P(x = 4) = 0.000169$

Therefore, there is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

8 0

2 years ago

Orlando has a loan with an effective interest rate of 7. 918%, compounded annually. Which of the following must be true? I. In t

svetlana [45]

The correct option is B, II. only.

Given to us,

I. In the effective rate formula, n is equal to one.

Effective interest rate formula,

$r = (1 + \dfrac{i}{n} )^n - 1.$

where,

r is the effective interest rate,

i is the stated interest rate,

n is the number of compounding periods per year.

According to the question the compounding periods per year is not given to us. Also, loans are taken for a longer period of time.

Thus, we can conclude that statement is false.

II. The nominal rate is 7. 918%.

nominal rate = real interest rate + inflation rate,

but as it is not mentioned in the question about the inflation rate. the statement is true to us. Assuming the inflation rate is 0%.

Thus, we can conclude that statement is true.

III. The Federal Funds Rate is static.

This statement is false, as the no information is given about this statement also this can not be concluded through assumption.

Thus, we can conclude that statement is false.

Hence, The correct option is B, II. only.

To know more visit:

brainly.com/question/15846526

4 0

3 years ago

How to simplifying linear expression

snow_lady [41]

To Simplify It Put It In Y=MX+B Form .

5 0

3 years ago

Nathaniel has $2 worth of dimes and quarters. He has 6 more dimes than quarters. By following the steps below, determine the num

Aleksandr-060686 [28]

Answer:

10 dimes and 4 quarters

Step-by-step explanation:

Number of dimes = d, each d = 10 c
Number of quarters = q, each q = 25 c
Total = $2 = 200 c

Equations according the given:

10d + 25q = 200
d = q + 6

Solve for q by substitution:

10(q + 6) + 25q = 200
10q + 60 + 25q = 200
35q = 140
q = 140/35
q = 4

Find the value of d:

d = 4 + 6 = 10

Nathaniel has 10 dimes and 4 quarters

8 0

3 years ago