2/9 of students in a school are in sixth grade.

The number of people arriving for treatment at an emergency room can be modeled by a Poisson Distribution with a rate parameter

AlekseyPX

Answer:

a) 0.052 = 5.2% probability that exactly three arrivals occur during a particular hour

b) 0.971 = 97.1% probability that at least three people arrive during a particular hour

c) 5.25 people are expected to arrive during a 45-min period

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Poisson Distribution with a rate parameter of seven per hour.

This means that $\mu = 7$

(a) What is the probability that exactly three arrivals occur during a particular hour?

This is P(X = 3).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 3) = \frac{e^{-7}*7^{3}}{(3)!} = 0.052$

0.052 = 5.2% probability that exactly three arrivals occur during a particular hour.

(b) What is the probability that at least three people arrive during a particular hour? (Round your answer to three decimal places.)

Either less than three people arrive, or at least three does. The sum of the probabilities of these events is 1. So

$P(X < 3) + P(X \geq 3) = 1$

We want $P(X \geq 3)$ , which is

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X \geq 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-7}*7^{0}}{(0)!} = 0.001$

$P(X = 1) = \frac{e^{-7}*7^{1}}{(1)!} = 0.006$

$P(X = 2) = \frac{e^{-7}*7^{2}}{(2)!} = 0.022$

So

$P(X \geq 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.001 + 0.006 + 0.022 + 0.029$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.029 = 0.971$

0.971 = 97.1% probability that at least three people arrive during a particular hour

(c) How many people do you expect to arrive during a 45-min period?

During an hour(60 minutes), 7 people are expected to arrive. So, using proportions:

$\frac{45*7}{60} = \frac{3*7}{4} = \frac{21}{4} = 5.25$

5.25 people are expected to arrive during a 45-min period

5 0

3 years ago

I am flooding these ( T_T)

dimulka [17.4K]

That should be 5 2/3 qt.

7 0

3 years ago

During a sale, a store offered a 20% discount on a TV that originally sold for $710. After the sale, the discounted price of the

Mademuasel [1]

Answer:

$681.60

Step-by-step explanation:

Given:

During a sale, a store offered a 20% discount on a TV that originally sold for $710. After the sale, the discounted price of the TV was marked up by 20%

To Find:

What was the price of the TV after the markup? Round to the nearest cent.

Solution:

$710 × (1 + 20%) × (1 - 20%)

$710 × 1.2 × (1-0.2)

$710 × 1.2 × 0.8

($710 × 1.2) × 0.8

852 × 0.8

= $681.60

Kavinsky

4 0

2 years ago

Plz help and give explaination of how to do it

professor190 [17]

Answer:

25% decreased by 60% is 10

Step-by-step explanation:

New value =

25 - Percentage decrease =

25 - (60% × 25) =

25 - 60% × 25 =

(1 - 60%) × 25 =

(100% - 60%) × 25 =

40% × 25 =

40 ÷ 100 × 25 =

40 × 25 ÷ 100 =

1,000 ÷ 100 = 10

hope this helps :)

7 0

3 years ago

Solve for the missing angle

vladimir2022 [97]

50-38=12
38+12=50
The answer is 12

7 0

3 years ago

2/9 of students in a school are in sixth grade.​

2/9 of students in a school are in sixth grade.