How do you figure out 3/2 divide 1/4=N. What is n between

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

Alonzo earns 8% commission on vacuum cleaner sales. This past month, Alonzo sold 70 units at $150.00 each. How much did Alonzo m

lilavasa [31]

Answer:

Made $840 in commissions for the past month.

Step-by-step explanation:

sales = 70 * 150 = 10500

commission = .08 * 10500 = 840

3 0

3 years ago

Read 2 more answers

The scale on a map is 1 cm: 7 km. If two cities are 15 cm apart on the map, what is the actual distance between the cities?

Lostsunrise [7]

Answer: C. 105 km

Step-by-step explanation:

By finding out that 1 cm is equal to 7 km, and that the two cities are 15 cm apart you can find it out by doing 7 x 15.

Enjoy. :)

5 0

3 years ago

Read 2 more answers

Hi piiihvvyjcycycfvyfchchv cgcydyfcyv fyiyifycgxt4w67 ftuddtyxd

Nataly_w [17]

Hello person above

How are you?

5 0

3 years ago

Find the greatest common factor 32a^3b^2, 44ab^3 and 40a^2b

Ronch [10]

$\32a^3b^2 \ , \ 44ab^3 \ , \ 40a^2b\\
$

$\text {Taking out common factor : } \\ \\
4ab(8a^2b) + 4ab(11b^2) + 4ab(10a)$

$\text { greatest common factor = } 4ab$

3 0

3 years ago