An exponential distribution is formed by the waiting times for a patient in the emergency room. The average waiting time for this distribution is 38 minutes. Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes? Round your answer to three decimal places.

Answers

Answer 1

Answer:

0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes

Step-by-step explanation:

To solve this question, we should understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The average waiting time for this distribution is 38 minutes.

This means that [tex]m = 38, \mu = \frac{1}{38} = 0.0263[/tex]

Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes?

Event A: Taking more than 37 minutes.

Event B: More than 37 + 41 = 78 minutes.

Probability of taking more than 37 minutes:

[tex]P(A) = P(X \leq 37) = 1 - e^{-0.0263*37} = 0.6221[/tex]

More than 37 minutes and more than 78 minutes:

The intersection is more than 78 minutes, so:

[tex]P(A \cap B) = P(X > 78) = e^{-0.0263*78} = 0.1286[/tex]

The probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1286}{0.6221} = 0.207[/tex]

0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes


Related Questions

calculate the GPA of a student with the following grades: B (3 hours), D (8 hours), C (18 hours). Note that an A is equivalent to 4.0, a B is equivalent to a 3.0, a C is equivalent to a 2.0, a D is equivalent to a 1.0, and an F is equivalent to a 0. Round your answer to two decimal places.

Answers

Answer:

The GPA of the student is 1.83.

Step-by-step explanation:

We use a weighted average to solve this question.

We have the following grades:

B, which is equivalent to 3, with weight 3.

D, which is equivalent to 1, with weight 8.

C, which is equivalent to 2, with weight 18.

So

[tex]M = \frac{3*3 + 1*8 + 2*18}{3 + 8 + 18} = \frac{53}{29} = 1.83[/tex]

The GPA of the student is 1.83.


Jimmy ate 1/3 of his sandwich at lunch. He ate another 2/3 of the sandwich. How much of the sandwich did Jimmy eat in all?
A.1/3
B.2/3
C.3/3
D.5/3

Answers

The answer is c (this needs too be 20 characters long)

The Gable Construction Corporation has placed bids for installing electronic message boards on two different highways.
Because of competition from other companies, Gable Construction Corporation officials estimate that the probability that
they will be awarded the Macon Expressway contract is 0.65 and the probability that they will be awarded the Seaview
Expressway contract is 0.43. Furthermore, the probability that they will be awarded both contracts is 0.22. What is the
probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

Answers

Answer:

0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

Step-by-step explanation:

We solve this question using these events as Venn sets.

I am going to say that:

Event A: Awarded the Macon Expressway.

Event B: Awarded the Seaview Expressway.

Probability that they will be awarded the Macon Expressway contract is 0.65

This means that [tex]P(A) = 0.65[/tex]

The probability that they will be awarded the Seaview Expressway contract is 0.43.

This means that [tex]P(B) = 0.43[/tex]

Furthermore, the probability that they will be awarded both contracts is 0.22.

This means that [tex]P(A \cap B) = 0.22[/tex]

What is the

Probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway?

Only A:

[tex]P(A) - P(A \cap B) = 0.65 - 0.22 = 0.43[/tex]

Only B:

[tex]P(B) - P(A \cap B) = 0.43 - 0.22 = 0.21[/tex]

Either

0.43 + 0.21 = 0.64

0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

Pls answer this for me​

Answers

Answer:

A) 216in squared

Step-by-step explanation:

6 / 2 = 3

4 * 3 = 12

12 * 2 = 24

5 * 12 = 60

60 * 2 = 120

6 * 12 = 72

24 + 72 + 120 = 216in^2

Hope this helped! Have a nice day! Plz mark as brainliest!!! :D

-XxDeathshotxX

please help i'm really stuck

Answers

how will apply the lesson i have learned in real life scenari

Pythagorean theorem

Answers

Answer:

a^2 + b^2 = c^2

Step-by-step explanation:

Answer:

a^2 + b^2 = c^2

Step-by-step explanation:

Used to find side lengths of right triangles, a and b represent sides, while c represents the hypotenuse.

Simplify the expression: 5(-5 + 2y) =

Answers

The answer is-25+ 10y

How many quarts are in two gallons?

Answers

2 gallons = 8 quarts

hope it's help ;3

ill so you the picture of it​

Answers

Answer:

Of WhaT?

Thanks for the free points btw

The equation x = 1 is an example of linear but not function. Why?

Answers

Because there is more than two y values for x = 1

If you buy 4 turkey subs that in total costs 26 dollars how much would 5 turkey subs cost.

Answers

Answer:

33/32.5

Step-by-step explanation:

26 divided by 4 equals 6.5

then 6.5 times 5 equals 32.5

Regina read his novel three nights in a row. Each night, he read for 3/4 of an hour. How many hours did regina read his novel altogether?​

Answers

Answer:

Regina read for 2 1/4 hours or 2 hours and 15 minutes

Step-by-step explanation:

He read for 2 hours and 15 minutes

more on fraction

21×5​

Answers

Answer:

105.

Step-by-step explanation:

21+21+21+21+21=105.

I just need help cause if I don’t I don’t know what imma do

Answers

Answer:

[tex]P(32) = \frac{1}{90}[/tex]

[tex]P(Odd) = \frac{1}{2}[/tex]

[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]

Step-by-step explanation:

Given

Sample Space = 10 to 99

First, we calculate the sample size (n)

[tex]n = 99 - 10 + 1[/tex]

[tex]n = 90[/tex]

Solving (a): P(32)

In 10 to 99, there is only 1 32.

So,

[tex]P(32) = \frac{n(32)}{n}[/tex]

[tex]P(32) = \frac{1}{90}[/tex]

Solving (b): P(Odd)

There are 45 odd numbers between 10 and 99

i.e.

[tex]n(Odd) = 45[/tex]

So:

[tex]P(Odd) = \frac{n(Odd)}{n}[/tex]

[tex]P(Odd) = \frac{45}{90}[/tex]

[tex]P(Odd) = \frac{1}{2}[/tex]

Solving (c): P(Multiple of 5)

There are 18 multiples of 5 between 10 and 99

i.e

[tex]P(Multiples\ 5) = \frac{18}{90}[/tex]

[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]

12cm and 8 cm find the ratio and reduce them in term of lowest term​

Answers

Answer:

very good im famous biol How to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerHow to add a great answerigist

Step-by-step explanation:

i need help with everything please if you help you are a legend please.

Answers

2. Closer to 0. Because it is always getting smaller. The smaller it gets, the closer it get to 0.

3.

a. Closest to 1.

b. Closest to 0.

c. (1/12)

4.

a. Closest to 1.

b. Closest to (1/2)

c. (14/16)-(10/16)=(4/16)

What’s the answer to this

Answers

The answer is A I think

Does anyone know the answer??????

Answers

Answer:

i think its the 2nd choice but im not 100% sure

Helpppppppppppppppppppppppppppppppp

Answers

Answer:

2/9 in the simplist form

Step-by-step explanation:

you multiply both the fractions for the area

then simplify

-2y + 4 > 10

solve the inequality

Answers

Step-by-step explanation:

-2y+4>10

subtract 4 from both sides

-2y+4-4>10-4

-2y>6

divide both sides by two

-2/2y>6/2

-1y>3

if negative y is greater than three than you have to multiply both sides of the equation by -1

y>-3 if you put that back into the earlier equation it is impossible.

so we have to switch the signs to < or less than

y<-3

Hope that helps:)

which is the least -1 1/4 or -3/2

Answers

Answer:

-3/2

Step-by-step explanation:

Please this will determine if I pass

Answers

The answer is B through ASA (Angle-Side-Angle) similarity criterion.

2 1/3 x 3 5/6 please answer

Answers

Answer:

8 17/18

Step-by-step explanation:

I used an online calculator (calculator soup)

Answer:

8 17/18

Step-by-step explanation:

7/3 * 23/6

7*23

3*6

161/18

8 17/18

Can someone write down the answers pls!!!!!!!!!!

Answers

Step-by-step explanation:

6b x>=1

6c y>7

7a x>3

7b -2<=2x<6

-1<=x<3

answer:-1,0,1,2,3

100 - 50 + 4

HELP PLS PLS PLSSSSS

Answers

Answer:

54

Step-by-step explanation:

100-50+4=50+4

=54

.....

6+x=23 what is x in the equation

Answers

the correct answer is x=17

Answer these correctly I’ll give brainalist + 10 points

Answers

first one is choice 1 second one is choice 3

heyy i need help on me hw​

Answers

Answer:

the answer is b

Step-by-step explanation:

brainliest pleasee?

Pierre found a new store where he hopes to save
money on his supplies. He bought 4 brushes and 7
tubes of paint for $32. He has another order for 6
brushes and 8 tubes of paint that will cost $43.
What is the cost of one brush? What is the cost of
one tube of paint?

Answers

Your first equation is 4x + 7y= 32, the x’s representing the brushes and the y’s the tubes of paint. Our second equation is 6x+8y=43. What I did is I multiplied the first equation by 1.5 so that it turns into 6x+10.5y=48. Then I subtracted the second equation from the first, canceling out the x’s and leaving us with 2.5y=5. Then divided and got y=2. We then go back to any of the original equations and plug it in to get the x’s.
6x+8(2)=43. We get 6x+16=43. We subtract and are left with 6x=27 and then x=4.5. Then plug both of them in to a different equation to double check. You could also use substitution by isolating one of the variables in one equation and then plugging it in to the other one.

What is the answer?
A)44
B)42
C)45
D)48

Answers

Answer:

44

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

because you take 3 pulse 2

Other Questions
How did the crickets lose their ability to chirp? Multiply. 37xy(35x3y2) Enter your answer in the box what makes up a conditional sentence PLEASEEE HELP ASAP ITS IMPORTANT !!!! Which is NOT a characteristic that all animals share? heterotrophs unicellular cells with a nucleus Pls help me pls Ill give brainliest pls dont answer if you dont know _____ is the term used to describe drugs that often lead to other serious and dangerous drug use. In paragraph 4 of the speech, how does Kennedy connect the ideas of the Industrial Revolution and modern inventions to the idea of space exploration? Why is Makenna (Robo en La Noche) going to Costa Rica? PLEASE HELP ME this is due today 2. Ella (vio, oy) un concierto. 3. Ella compr las entradas en (la pelcula, la taquilla). 4. Ella (entendi, aprendi) la pelcula porque estudia espaol en la escuela. 5. Dan (una estatua, una exposicin) en el museo. can someone answer the correct completions This issue was debated at the Constitutional convention and was left unsolved for future generations What pattern do you see developing in the ancient world? GUYS PLEASE HELP ME I BEG YOU The two lines represent the distance traveled, over time, by two trains. Which train is traveling more quickly? Answer if you know the answers or some answers to "The Four Skillful Brothers" . The pic is to show what im talking about o change.day.3 The president opened theay cake was4 Versace will design then5 They didn't give me anyure6 They produce the clothe:ve is madearticiple ofReflexive pronouns; each other1 Complete the sentences with the correctreflexive pronoun or each other.My sister has gone shopping. She's going tobuyherselfsome new nail varnish.1 Don't worry about me. I'm OK. I can lookafter2 You mustn't blamefor theaccident, Ellen. It wasn't your fault.3 At Christmas, my sister and I always givepresents.4 Thank you for the wonderful party. We reallyenjoyed5 Oliver is a very quiet boy. He doesn't knowhow to express6 Our cat has taughthow topush the door open.for7 My parents have knownover thirty years.is madeastPassive: past, present an4 Complete the sentences wpassive form of the verbs iThey weren't paid last Frid1 This suitbfor last year's fashion sh2 If we arrive late tonighttickets for the show. (no3 Every year, a lot of oranfrom Spain. (export)4 Next year, the shoessive isthe past You have 10 coins, all dimes and quarters. The valueof the coins is $1.75.How many dimes do you have?How many quarters do you have? 50 POINTS!!!!!Question 1 (1 point) SavedWhich desert is found in SUB-Saharan AfricaQuestion 1 options:SaharaNamibGobiAtacamaQuestion 2 (1 point) SavedMany of the countries in Sub-Saharan are ___________________which limits their tradeQuestion 2 options:Culturally dividedMineral strongDevelopedLandlockedQuestion 3 (1 point) Which river can NOT be found in Sub-Saharan Africa?Question 3 options:NigerNileZambeziPlatteQuestion 4 (1 point) Most of Sub-Saharan Africa is composed of Question 4 options:DesertsRainforestsJunglesHuge plateaus and escarpmentsQuestion 5 (1 point) Which of the following is NOT a city of culture and trade in Sub-Saharan Africa?Question 5 options:GazaDakarLagosJohannesburgQuestion 6 (1 point) Famous falls found in Sub-Saharan AfricaQuestion 6 options:Angel FallsVictoria FallsNiagara FallsLake TanganyikaQuestion 7 (1 point) Area where two tectonic plates are moving away from one anotherQuestion 7 options:Mt. KilimanjaroGreat Rift ValleyRing of FireVictoria FallsQuestion 8 (1 point) Line of Latitude that bisects the continent of Africa causing the climates north and south of the line to be similarQuestion 8 options:Tropic of CapricornTropic of CancerPrime MeridianEquatorQuestion 9 (1 point) Environmental problem caused by over-grazing in Sub-Saharan AfricaQuestion 9 options:DesertificationSahelDeforestationGlobalizationQuestion 10 (1 point) ____________________or tropical wet/dry climates where you can find nature preserves or parksQuestion 10 options:ValleySahelSavannaDesert What was the impact of the peace of Paris on native people?