Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. According to a 2017 large-scale study of elderly ICU patients, the average length of stay in the ICU is 3.4 days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations.

a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)?

b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)?

c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?

Answers

Answer 1

Using the exponential distribution, it is found that there is a:

a) 0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.

b) 0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.

c) 0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.

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) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

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

In this problem, the mean is of 3.4 days, hence, the decay parameter is:

[tex]\mu = \frac{1}{3.4}[/tex]

Item a:

[tex]P(X \leq 1) = 1 - e^{-\frac{1}{3.4}} = 0.2548[/tex]

0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.

Item b:

[tex]P(X \leq 2) = 1 - e^{-\frac{2}{3.4}} = 0.4447[/tex]

[tex]P(X \leq 3) = 1 - e^{-\frac{3}{3.4}} = 0.5862[/tex]

[tex]P(2 \leq X \leq 3) = 0.5862 - 0.4447 = 0.1415[/tex]

0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.

Item c:

[tex]P(X > 5) = e^{-\frac{5}{3.4}} = 0.2298[/tex]

0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.

A similar problem is given at https://brainly.com/question/17039711


Related Questions

The width of a rectangle is 6 kilometers
a
less than twice its length. If its area is
56 square kilometers, find the
dimensions of the rectangle.

Answers

Answer:

9,333333333333333 and 6 Km

Step-by-step explanation:

The width of a rectangle is 6 kilometers

less than twice its length. If its area is

56 square kilometers, find the

dimensions of the rectangle.

the area of ​​the rectangle is found by multiplying the width by the height, you have the area and the width, divide the area by the width and find the length

56 : 6 = 9,333333333333333 Km

-----------------------------

check

9,333333333333333 * 6 = 56

the answer is good

10% of $70 = what is the answer i do not now it.

Answers

Answer:

10% 0f 70 is 7

Step-by-step explanation:

70÷10=7

10%=7

It is 9 kilometers from Charlie's house to the nearest mailbox. How far is it in meters?
Be sure to include the correct unit in your answer.

Answers

Answer:

Step-by-step explanation:

9,000 meters

We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)

Evaluate the information given by the pilot.
Show calculations to support your answer.

Answers

Answer:

Step-by-step explanation:

500 mph with a flight time of 10 hours and 20 minutes  [(20 min)*(1 h/60 min) = 0.333 hr]

Distance = Speed * Time

Time = 10.333 hours

Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles

The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles.  That is a 4.3% reduction from the pilot's numbers.  Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.

My preference would be to trust the pilot's data.  I don't know where Mark got his math education.

Maya earned $225.oo at her job when she worked for 10 hours. What did she earn in one hour?

Answers

$22.50 an hr because 225 divided by 10 is 22.5

Compute the integral Z Z Z U y dV , where U is the part of the ball of radius 2, centered at (0, 0, 0), that lies in the 1st octant. Recall that the first octant is the part of the 3d space where all three coordinates x, y, z are nonnegative. (Hint: You may use cylindrical or spherical coordinates for this computation, but note that the computation with cylindrical coordinates will involve a trigonometric substitution - so spherical cooridnates should be preferable.)

Answers

As the hint suggests, convert to spherical coordinates using

x = p cos(u) sin(v)

y = p sin(u) sin(v)

z = p cos(v)

dV = dx dy dz = p² sin(v) dp du dv

Then U is the set

[tex]U = \left\{ (p,u,v) \mid 0\le p\le2 \text{ and } 0\le u\le \dfrac{\pi}2 \text{ and } 0\le v\le\dfrac{\pi}2\right\}[/tex]

and the integral of y over U is

[tex]\displaystyle \iiint_U y \, dV = \iiint_U p\sin(u)\sin(v) \cdot p^2 \sin(v) \, dV[/tex]

[tex]\displaystyle \iiint_U y \, dV = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \int_0^2 p^3 \sin(u) \sin^2(v) \, dp \, du \, dv [/tex]

[tex] \displaystyle \iiint_U y \, dV = \frac{2^4-0^4}4 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \sin(u) \sin^2(v) \, du \, dv [/tex]

[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \left(-\cos\left(\frac\pi2\right) + \cos(0)\right) \int_0^{\frac\pi2} \sin^2(v) \, dv [/tex]

[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \frac12 \int_0^{\frac\pi2} (1-\cos(2v)) \, dv [/tex]

[tex]\displaystyle \iiint_U y \, dV = 2 \left(\left(\frac\pi2 - \frac12 \sin\left(2\cdot\frac\pi2\right)\right) - \left(0 - \frac12 \sin\left(2\cdot0\right)\right) \right)[/tex]

[tex]\displaystyle \iiint_U y \, dV = \pi - \sin(\pi) = \boxed{\pi}[/tex]

what is 1 1/2 of 150 and what is 1/2 of 180 ​

Answers

Answer:

1 1/2 of 150 is 225 and 1/2 of 180 is 90

Step-by-step explanation:

1 1/2 of 150 basically means 1 1/2 x 150, which equals to 225. 1/2 of 180 means 1/2 x 180 which is 90.

Answer:

1 1/2 of 150 is "225" and

1/2 of 180 is "90"

Step-by-step explanation:

1 1/2 of 150 basically means 1 1/2 x 150, which equals to 225. 1/2 of 180 means 1/2 x 180 which is 90.

Hope this helps :)

HELP! Can anyone help me i need help it this question

Answers

Average rate = distance / time

Rewrite distance as an improper fraction":3 1/3 = 10/3

Now you have 10/3 / 1/3

When dividing by a fraction flip the second fraction over and multiply:

10/3 x 3/1 = (10 x 3) / (3/1) = 30/3 = 10

Average rate was 10 miles per hour

pls help with khan academy

Answers

Answer:

c

Step-by-step explanation:

because the rest are just way off

Answer:

The answer is C, bro

Step-by-step explanation:

hope this helped.

What is 11 divided by 1/4

Answers

44 i think if not really sorry

here is the other question

Answers

Answer:

1. -3 × A1 + A2 --> B2

2. [tex]-\frac{1}{7}[/tex] × B2 --> C2

Step-by-step explanation:

1. -3 × A1 + A2 --> B2

(4x × -3) + 12x = -12x + 5x = -7x

(2y × -3) + 6y = -6y + 6y = 0y

(-10 × -3) + -9 = 30 - 9 = 21

2. [tex]-\frac{1}{7}[/tex] × B2 --> C2

-7x × [tex]-\frac{1}{7}[/tex] = 1x

21 × [tex]-\frac{1}{7}[/tex] = -3

Same process as last time

Solve for x: -2(x + 3) = -2x - 6

A. 0
B. 3
C. All real numbers
D.No solution

Answers

Answer:

D.No solution

Answer:

C

Step-by-step explanation:

-2(x + 3) = -2x - 6               Remove the brackets

-2x - 6 = -2x - 6

Since the left and right sides are equal, any number will work.

If you wind up with a false statement, then there are no solutions.

2x + 4 = 2x + 7                    Subtract 2x from both sides.

4 =    7

in which system are the lines parallel ?

Answers

Answer: B

explanation: the slope is the same in both equations

which of the following does not require the use of chain rule to find dy/dx.

Answers

C. For each term in this expression, you can just apply the power rule.

[tex]y = 3x^2 - \sqrt x + \dfrac2x = 3x^2 - x^{\frac12} + 2x^{-1}[/tex]

[tex]\implies \dfrac{dy}{dx} = 2\cdot3x^{2-1} - \dfrac12 x^{\frac12-1} + (-1)\cdot2x^{-1-1}[/tex]

[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac12 x^{-\frac12} - 2x^{-2}[/tex]

[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac1{2\sqrt x} - \dfrac2{x^2}[/tex]

Every other choice involves composite functions that do require the chain rule to differentiate.

Option C  : [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]  can be differentiated without using chain rule.

The differentiation of  [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   without using chain rule can be done as follows:

[tex]\begin{aligned}\dfrac{dy}{dx} &= \dfrac{d}{dx}(3x^2 - \sqrt{x} + \dfrac{2}{x})\\\\&= \dfrac{d}{dx}(3x^2 - x^{\frac{1}{2}} + 2x^{-1})\\&= 6x - (1/2)x^{-\frac{3}{2}} -2x^{-2}\\\end{aligned}[/tex]

The rest of the functions are composite, which means, that after differentiating them with some other base, you need to change the base and differentiate again, thus applying chain rule.

Thus, the function [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   can be differentiated without using chain rule.

Thus, option C:   [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   is correct option.

Learn more here:

https://brainly.com/question/5543508

Find one value of x for F(x)=-4

Answers

F(x) = -4 means y = -4. That means whatever the x is, the answer is going to be -4.

Multiplying polynomials

Answers

Steps are in the attachment.

________

Hope it helps :)) ⚜

the probability that a tin of paint is dented is 0.07 out of 3000 tins of paint,how many would you expect to be dented?

Answers

Answer:

3000×0.07=210 tins

Step-by-step explanation:

210 tins

Step-by-step explanation:

3000÷100×0.07

=2.1

MARK ME BRAINLIEST PLS!!

Can some please help me I will mark u brilliant

Answers

Question 2: -4/3

Question 3: -7/20

PLEASE ANSWER ASAP (no links please)
Solve for the indicated variable


g/h = e - 10 for g

Answers

Answer:

g = he - 10h

Step-by-step explanation:

A company that bakes chocolate chip cookies averages 5.2 chocolate chips per cookie. Assume that the number of chocolate chips per cookie follows the Poisson distribution. What is the probability that a randomly selected cookie will contain two or more chocolate chips

Answers

Answer 12

Step-by-step explanation:

A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four units, and because each has identical packaging, the selection will be random. What is the probability that (a) all four units are good, (b) exactly two units are good, and (c) at least two units are good?

 I hope that helped?

What is the volume, in cubic inches, of a rectangular prism with a height of 7 inches, a width of 10 inches, and a length of 9 inches?

Answers

Answer:

Step-by-step explanation:

87

Answer:

630 in.³

Step-by-step explanation:

To find the volume of a rectangular prism, you can multiply the height, times the width, times the length. So, let's go ahead and do that with the values of the given prism.

7 × 10 × 9 = 70 × 9 = 630

So, our volume is 630...but not so fast. We also have to put in our units. Our units are inches × inches × inches, or inches³. So our final value is 630 in.³

Hopefully that's helpful! :)

2 short questions
Please help

Answers

Answer:

b c = 5.25p this is the answer

For the first problem shown the answer is number B.

It is B because we our always going up by $5.25

For our second one it isn't a function,

it isn't a function because it follows the same rule through-out it besides at the end of it.

Five students share the writing of a term
paper evenly. If each person writes more
than six pages, how long is the paper?

Answers

Answer:

Over 30

Step-by-step explanation:

There is no definite answer if you don't know how many pages each person. All you have to do is multiply 5 by 6

30. What is the solution to the system of equations?

3x + 3y - Z=1
Z=8
-X-3y + 2z = 13


A: (3, 0, 8)

B: (3, 0, -8)

C: (-3, 0,8)

D: (3, 2, 8)

Answers

Answer:

x = 3

y = 0

z = 8

Step-by-step explanation:

a) 3x + 3y - z = 1

b) z = 8

c) -x -3y + 2z = 13

a) 3x + 3y - 8 = 1 (substitution)

a) 3x + 3y = 9

c) - x - 3y + 2(8) = 13 (substitution)

c) -x - 3y + 16 = 13

c) -x - 3y = -3

(3x + 3y = 9) + (-x -3y = -3)

= 2x = 6

x = 3

a) 3(3) + 3y - 8 = 1

9 + 3y - 8 = 1

y = (1 -9 + 8)/3

y = 0

Either enter exact answer in terms of pie or 3.14

Answers

Answer:

18 π ≈ 56.52

Step-by-step explanation:

The formula for the volume of a cylinder is V = π · r² · h.

This cylinder has a height (h) of 2 and a radius (r) of 3.

Therefore the volume is:

V =  π · r² · h = π · 3² · 2 = 18 π ≈ 56.52.

I need to know how to subtract fractions 4 2/3 - 3/4

Answers

Answer: The answer would be 3.91666666667

[tex]\huge\textsf{Hey there!}[/tex]


[tex]\mathsf{4 \dfrac{2}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{4\times3+2}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{12 + 2}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{14}{3} - \dfrac{3}{4}}[/tex]

[tex]\mathsf{= \dfrac{56}{11} - \dfrac{9}{12}}[/tex]

[tex]\mathsf{= \dfrac{14\times4}{12 - 0}}[/tex]

[tex]\mathsf{= \dfrac{56 - 9}{12}}[/tex]

[tex]\mathsf{= \dfrac{47}{12}}[/tex]

[tex]\mathsf{= 3 \dfrac{11}{12}}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: }\huge\boxed{\\\mathsf{\dfrac{47}{12} \ or\ 3 \dfrac{11}{12}}}\huge\checkmark[/tex]



[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]



~[tex]\frak{Amphitrite1040:)}[/tex]


The graph of the function f(x) = (x + 2)(x + 6) is shown
below.
Which statement about the function is true?
O The function is positive for all real values of x where
x>-4.
6
14-
O The function is negative for all real values of x where
-6 < x < -2.
The function is positive for all real values of x where
x <-6 orx > -3.
O The function is negative for all real values of x where
x < -2.
24
-2
2
4
6
х
4

Answers

Answer:

The function is negative for all real values of x where

-6 < x < -2.

Step-by-step explanation:

f(x) = (x +2)(x + 6)

 x + 2 = 0    or   x + 6 = 0

x = -2     or x = -6

 After graphing the function is negative between -6 < x < -2

The true statement about the graph is (a) The function is negative for all real values of x where -6 < x < -2.

The equation of the function is given as:

[tex]f(x) = (x + 6)(x + 2)[/tex]

From the graph, we have the following highlights

The values of the function decreases from negative infinity till x = -4The values of the function increases from x = -4The values of the function is negative for x = -6 to x = -2

The above means that:

The function is negative for all real values of x where -6 < x < -2.

Hence, the true statement about the graph is (a)

Read more about quadratic graphs at:

https://brainly.com/question/7988424

Robert has 4 times as many pennies as he does nickels. If Robert has $1.44 worth of pennies and nickels, how many nickels does he have?​

Answers

He is going to have 21 nickels

Umm how to do rates

Answers

The definition of a rate in math is, the speed of something being gained in a problem, let's say we have a hot pipe that can full up a pool in 6 hours, our rate would be 1/6 of the pool per hour.

Find the length of the hypotenuse, side c, of a right triangle with legs of length a = 4 and b = 5. Use a calculator to estimate the
square root to one decimal place.

Answers

answer:

6.4

Step-by-step explanation:

4^2+5^2=c^2

16+25

square root of 41

c^2=6.4

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