2. Patients arrive at a hospital accident and emergency department at random follow a
Poisson distribution at a rate of 6 per hour.
(a) Find the probability that, during any 90-minute period, the number of patients
arriving at the hospital accident and emergency department is
(i) exactly 7
(2 marks)
(ii) at least 3
(2 marks)
(b) What is the mean and standard deviation of the number of patients arriving at the
hospital accident and emergency department in an hour?
(2 marks)

Answer:

0.11711612445;

0.99376780489;

2.4494897

Step-by-step explanation:

Given that :

Arrival rate = 6 per hour

Mean Arrival during 90 minute period :

60 min = 6

90 min = (6 * 90) / 60 = 9

λ = 9

Using poisson :

P(x =x) = (e^-λ * λ^x) / x!

1) Exactly 7

P( x = 7) = (e^-9 * 9^7) / 7!

= 590.26526724266 / 5040

= 0.11711612445

Atleast 3:

P(x ≥ 3)

P(x ≥ 3) = 1 - P(x < 3)

P(x < 3) = p(x =0) + p(x = 1) + p(x = 2)

P(x = 0) = (e^-9 * 9^0) / 0! = 0.0001234098

P(x = 1) = (e^-9 * 9^1) / 1! = 0.00111068824

P(x = 2) = e^-9 * 9^2) / 2! = 0.00499809707

1 - P(x < 3) =

1 - (0.0001234098 + 0.00111068824 + 0.00499809707)

1 - 0.00623219511

= 0.99376780489

B.) mean and standard deviation of the number of patients arriving at the hospital accident and emergency department in an hour?

Mean = arrival per hour = λ = 6

Standard deviation = √λ = √6

Standard deviation = 2.4494897

The probability that, during any 90-minute period, the number of patients  arriving at the hospital accident and emergency department is exactly 7 is 0.11711612445 and the probability for at least 3 is 0.99376780489. The mean is 6 and the standard deviation is 2.4494897.

Given :

Patients arrive at a hospital accident and emergency department at random follow a  Poisson distribution at a rate of 6 per hour.

Accprding to the poisson distribution:

[tex]\rm P(x=x)=\dfrac{(e^{-\lambda} \times \lambda^x )}{x!}[/tex]

a) The probability that, during any 90-minute period, the number of patients  arriving at the hospital accident and emergency department is:

First, determine the value of [tex]\lambda[/tex]:

[tex]\lambda = \dfrac{6\times 90}{60} = 9[/tex]

(i) At (x = 7) the probability is given by:

[tex]\rm P(x=7)=\dfrac{(e^{-9} \times 9^7 )}{7!}[/tex]

Simplify the above expression.

P(x = 7) = 0.11711612445

(ii) At (x [tex]\geq[/tex] 3) the probability is given by:

[tex]\rm P(x\geq 3)=1-P(x<3)[/tex]

[tex]\rm P(x\geq 3)=1-P(x=2)-P(x=1)-P(x=0)[/tex]

[tex]\rm P(x=2)=\dfrac{(e^{-9} \times 9^2 )}{2!}=0.00499809707[/tex]

[tex]\rm P(x=1)=\dfrac{(e^{-9} \times 9^1 )}{1!}= 0.00111068824[/tex]

[tex]\rm P(x=0)=\dfrac{(e^{-9} \times 9^0 )}{0!}= 0.0001234098[/tex]

So, the probability at (x [tex]\geq[/tex] 3) is given by:

[tex]\rm P(x\geq 3)=1-0.0001234098 - 0.00111068824 - 0.00499809707[/tex]

[tex]\rm P(x\geq 3)=1 - 0.00623219511[/tex]

[tex]\rm P(x\geq 3)= 0.99376780489[/tex]

b) The mean and standard deviation of the number of patients arriving at the  hospital accident and emergency department in an hour are given by:

[tex]\rm Mean = \lambda = 6\\\\[/tex]

[tex]\rm Standard\; Deviation=\sqrt{\lambda }= \sqrt{6} = 2.4494897[/tex]

For more information, refer to the link given below:

https://brainly.com/question/17716064

round 427,266 to the nearest ten thousand​

how many tens should be added to 56 to get 506​

Is this relation a function?
(2, -3), (-4, 2), (6,2), (-5, -3), (-3,0)

Population density is a measure of how crowded an area is. The population density of Australia is approximately 7.6 people per square mile. If Bangladesh has 2,949.7 more people per square mile than Australia, what is the population density of Bangladesh?
2942.10 people per square mile
2957.30 people per square mile
3025.70 people per square mile
3709.70 people per square mile

The GCF of 24 and 40 is _______. Numerical Answers Expected! Answer for Blank 1:

find the slope of the line that contains the points (-6, 4) and (2, -8)

if you answer correctly u get brainliest

Look at the Employee Time Card for
Gwen Ramirez. If Gwen's hourly wage is
$12.00 how much money did she make on
Tuesday?
$84.00
$64.00
$84.50
$96.00

Michelangelo buys a computer for $400. He is charged a 6% tax.


How much is just the tax?


How much is the total?

pls show work

14 sandwiches and 3 drinks cost €33.75. 6 sandwiches and 17 drinks cost €26.25 . How much cost 1 sandwich and 1 drink

In the first 1/3 hour of a snow storm, 1/12 of an inch or snow fell. If the snow continues to fall at the same rate, how many inches of snow will fall in 2 hours?

Michaela rode her bike on 14 2/3 mile trail. She stopped every 3 1/5 miles for a drink of water . Issac and Jake estimated how many times Michaela stopped.

Who is in NMUSD school district

Landon was taking a math test he finished 1/2 of the test in 357 hour how much of the test will he have done in one hour if he keeps the same pace

A 14 inch pizza is cut into 8 slices. What is the area of each slice?(sector area)

The graph of the function f is shown, f(5)=

Ben is an Accounts Payable clerk and has specific instructions from the controller to print 4 reports twice a day on day 1, then 3 of those reports twice a day on days 2 through 6, then on the final day,1 of those reports twice a day. How many reports will Ben print in 7 days?

in the following diagram BC is parallel to DE. What is the mesure of x?

Complete the coordinate proof of the theorem. Given: A B C D is a rectangle. Prove: The diagonals of A B C D are congruent.
Art: A rectangle is graphed on a coordinate plane. The horizontal x-axis and vertical y-axis are solid. The vertex labeled as A lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as B lies on begin ordered pair a comma 0 end ordered pair. The vertex labeled as D lies on begin ordered pair 0 comma b end ordered pair. The vertex C is unlabeled. Diagonals A C and B D are drawn by dotted lines.

The coordinates of rectangle ABCD are A(0, 0), B(a, 0), C( , ), and D(0, b). The length of AC⎯⎯⎯⎯⎯ is equal to . The length of BD⎯⎯⎯⎯⎯ is equal to . The diagonals of the rectangle have the same length. Therefore, AC⎯⎯⎯⎯⎯ is congruent to BD⎯⎯⎯⎯⎯.

someone please help me with this ​

Angle 6 and angle 7 are related by

Can someone help please

How many decimal places will there be in the product shown below? 23.58 x 14.2 = ?

Using the given sets of points, identify slope (m), y-intercept (b), and write the equation. (0, 4) and (-1, -1)

Please help will give you 20 points :)

The ratio of Monarch butterflies to Queen butterflies at a butterfly farm was 9:7. If there are no additional butterflies at the farm, what is the ratio of Queen butterflies to the total number of butterflies at the farm? (5 points)


9:16

16:9

16:7

7:16

Which graph best represents a line with a slope of
?

Evaluate-5X 6 =
(Need help)

What is the median for 6.0 6.0 7.0 7.0 8.0 9.0

Write an equation of a line in slope intercept form that is parallel to y = -3x+9 and passes through the point (-2,-5)

Need help


Giving brainliest