Ask question

Ask question

All categories

19 days ago

11

Radio blackouts are among the most common space weather events to affect Earth. Minor radio blackouts occur, on average, twice p

er year. Use a Poisson process to model the phenomenon. (a) Given that 3 events have occurred in the first half of the year, what is that probability that 3 events will happen in the rest of the year? (b) How many radio blackouts do you expect to see in two years? (c) Starting from now, how long must we wait so that the probability of seeing the next radio blackout is at least 0.5? (d) Find the probability that the time to the 4th blackout is at most 2 years.

1 answer:

Zina [9.1K]19 days ago

8 0

Answer:

a. P(x = 3) = 0.061313

b. The anticipated number of radio blackouts = 4

c. It's unclear when the next radio blackout will occur.

d. P(x = 4) = 0.19537

Step-by-step explanation:

Based on the provided details:

A Poisson process is utilized to model the occurrence of this event:

Minor radio blackouts occur, on average, two times annually.

Therefore:

$\lambda = 2 \ years$

For question (a)

time t = 1/2 (i.e., six months)

Let x represent the likelihood of 3 incidents during the remaining months of the year.

Then:

$P(x = 3) = \dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!}$

$P(x = 3) = \dfrac{e^{-2* 0.5} \times (2 * 0.5)^3}{3!}$

P(x = 3) = 0.061313

b).

The expected number of radio blackouts over two years is calculated as follows:

We start with:

t = 2 years

E(x) = λ × t

E(x) = 2 × 2

E(x) = 4

Thus, the predicted number of radio blackouts = 4

c).

The time we must wait until the probability of witnessing the next radio blackout reaches at least 0.5 is as follows:

In this case, time (t) =???

Thus:

P(x =1) = 0.5

$P(x = 1) = \dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5$

$\dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5$

Consequently, we are unable to ascertain the probability (50%) of the next radio blackout.

d)

We can compute the probability that the time until the fourth blackout is at most 2 years as follows:

Here;

x =4, t = 2

Thus:

$P(x = 4) = \dfrac{e^{-4 } \times (4)^4}{4!}$

P(x = 4) = 0.19537

You might be interested in

Create a pattern for the rule a x 3 + 2

Inessa [9000]

A sequence for this rule can be established by beginning with the number one and consistently applying the rule to each following number: 1 x 3 + 2 = 5, 5 x 3 + 2 = 17, 17 x 3 + 2 = 53, etc.

3 0

4 days ago

Julia owns a coffee shop. She experimented with mixing City Roast Colombian coffee that costs $7.80 per pound with French Roast

PIT_PIT [9117]

Answer:

8 lb of French Roast and 12 lb of City Roast coffee

Step-by-step explanation:

In this scenario, we identify two variables: the weight of City Roast coffee (denote as "C") and that of French Roast coffee (denote as "F")

The first equation we create pertains to the overall weight of the coffee (20 lb total), represented by C and F as follows:

first equation C + F = 20

Subsequently, we derive another equation regarding the mixture's cost. Each pound of City Roast costs $7.80, so for C pounds, the cost becomes $7.80 * C

For the French Roast—priced at $8.10 per pound—we deduce that F pounds will cost $8.10 * F

The total of these costs should equal the desired total for the 20 lb blend: $7.92 * 20 = $158.4

We format the total cost equation as follows:

$7.80 * C + $8.10 * F = $158.4

Next, we use the first equation to express one variable in terms of the other, allowing us to solve for "C":

C + F = 20

C = 20 - F

We then replace "C" in the second equation with this expression:

7.80 (20 - F) + 8.10 F = 158.4

7.80 * 20 - 7.80 F + 8.10 F = 158.4

Combining the F terms results in + 0.3 F

156 + 0.3 F = 158.4

Isolating F results in:

0.3 F = 158.4 - 156 = 2.4

Dividing both sides by 0.3 yields:

F = 2.4 / 0.3 = 8

This indicates that we need 8 pounds of French Roast coffee.

Consequently, the remainder (12 lb) should consist of the City Roast.

5 0

14 days ago

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the

Inessa [9000]

Response:

45.54m

Step-by-step breakdown:

See the provided figure

Scarlett's height is represented as AB = 1.65 meters

She stands 90 meters away from the dam, so BE = AC = 90 m

Scarlett measures the angle of elevation to the dam's summit at 26º, which is ∠DBE = 26°

Height of the Dam = DC = EC+DE

AB = EC = 1.65

In triangle BDE

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan 26^{\circ} = \frac{DE}{BE}$

$Tan 26^{\circ} = \frac{DE}{90}$

$0.48773 \times 90=DE$

$43.89=DE$

Height of the Dam = DC = 1.65 + 43.89 = 45.54 m

Therefore, the dam's height is 45.54 m.

7 0

28 days ago

Read 2 more answers

) If the pattern shown continues, how many black keys appear on a portable keyboard with 49 white keys? Suggestion: use equivale

Zina [9171]

There are 5 black keys for each 7 white keys. Hence, the ratio stands at 5:7. To determine how many black keys correspond to 49 white keys, we calculate the scaling factor for the ratio: 49 divided by 7 equals 7. Thus, the original ratio is scaled by 7. Therefore, the total number of black keys equals 5 multiplied by this scaling factor, resulting in 35 black keys.

5 0

4 days ago

Read 2 more answers

An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest

AnnZ [9099]

$\bf \qquad \textit{Amount for Exponential Decay}\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &730\\
r=rate\to 28.8\%\to \frac{28.8}{100}\to &0.288\\
t=\textit{elapsed time}\to &10\\
\end{cases}
\\\\\\
A=730(1-0.288)^{10}\implies A=730(0.712)^{10}$

6 0

11 days ago

Read 2 more answers