Starting at 6 a.m. every morning, Matilda receives text messages on her cell phone from her mother, her best friend, and her brother according to three independent Poisson processes. Her mother texts Matilda on average once every hour. Her best friend sends a message once every 10 minutes, and she receives messages from her brother every 30 minutes.
A) Find the probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.
B) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

Answers

Answer 1

Answer:

a) 0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

b) [tex]1.6 \times 10^{-9}[/tex] probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

Step-by-step explanation:

Poisson distribution:

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

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

A) Find the probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

Two from the best friend:

Her best friend sends a message once every 10 minutes.

From 6 to 7:30, there is an hour and a half, that is, 90 minutes, so the mean for her best friend is [tex]\mu = \frac{90}{10} = 9[/tex]

Two messages is P(X = 2). So

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

[tex]P(X = 2) = \frac{e^{-9}*9^{2}}{(2)!} = 0.0050[/tex]

Two from the mother:

Message every hour = 60 minutes. So [tex]\mu = \frac{90}{60} = 1.5[/tex]. This is P(X = 2).

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

[tex]P(X = 2) = \frac{e^{-1.5}*1.5^{2}}{(2)!} = 0.2510[/tex]

Two of her best friend and two of her mother:

Independent events, so the probability of both happening is the multiplication of their separate probabilities.

[tex]p = 0.005*0.251 = 0.0013[/tex]

0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

B) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

In 3 hours, she is expected to receive:

3*60/10 = 18 messages from her best friend.

3*60/60 = 3 messages from her mother.

3*60/30 = 6 messages from her brother.

In total, 27 messages.

75% probability of a typo, so [tex]\mu = 0.75*27 = 20.25[/tex]

This is P(X = 0).

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

[tex]P(X = 0) = \frac{e^{-20.25}*20.25^{0}}{(0)!} = 1.6 \times 10^{-9}[/tex]

[tex]1.6 \times 10^{-9}[/tex] probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.


Related Questions

Ophelia reads 104 pages in 2 hours, how many pages will she read in 3 hours? REMEMBER TO INCLUDE THE UNIT OF MEASURE (PAGES)
IN YOUR ANSWER.
eb9th
m 12:00
Your answer:

Answers

Answer:

156 pages.

Step-by-step explanation:

Ophelia's reading speed is 104 pages / 2 hours = 52 pages/hour. So in 3 hours she will have read 3 * 52 = 156 pages.

Find the volume
I really need your help

Answers

Answer:

[tex] V_{total} = 26460 \pi~cm^3 [/tex]

[tex] V_{total} = 83127~cm^3 [/tex]

Step-by-step explanation:

The solid is made up of 2 cones and a cylinder.

Upper cone:

radius = 21 cm

height = h_1 = 70 cm - 35 cm = 35 cm

Cylinder:

radius = 21 cm

height = h_2 = 35 cm

Lower cone:

radius = 21 cm

height = h_3 = 40 cm

[tex] V_{total} = V_{upper~cone} + V_cylinder} + V_{lower~cone} [/tex]

[tex] V_{total} = \dfrac{1}{3} \pi r^2 h_1 + \pi r^2 h_2 + \dfrac{1}{3} \pi r^2 h_3 [/tex]

[tex] V_{total} = \dfrac{1}{3}(\pi)(21~cm)^2(35~cm) + (\pi)(21~cm)^2(35~cm) + \dfrac{1}{3}(\pi)(21~cm)^2(40~cm) [/tex]

[tex] V_{total} = \dfrac{1}{3}(\pi)(441~cm^2)(35~cm) + (\pi)(441~cm^2)(35~cm) + \dfrac{1}{3}(\pi)(441~cm^2)(40~cm) [/tex]

[tex] V_{total} = (147~cm^2)(35~cm)(\pi) + (441~cm^2)(35~cm)(\pi) + (147~cm^2)(40~cm)(\pi) [/tex]

[tex] V_{total} = 5145\pi~cm^3 + 15435\pi ~cm^3 + 5880\pi~cm^3 [/tex]

[tex] V_{total} = 26460 \pi~cm^3 [/tex]

[tex] V_{total} = 83127~cm^3 [/tex]

HELP PLEASE URGENT TIMED

Answers

Answer:

Step-by-step explanation:

-6(x - 7)
Help Please

Answers

The answer for -6(x - 7) will be -6x + 42

Answer:

-6x + 42

I distributed the -6

Which value is a solution of the inequality 9 >_ 1/2x
18
20
24
36

Answers

the first one (18) is the answer

Jay jogs daily for exercise. he hits faster than 3.5 miles per hour every day. which inequality representd Jay's jogging speeds s?

Answers

Answer:

B

Step-by-step explanation:

The speed each day is faster than 3.5. Otherwise known as the mileage covered each day.

how does 9+10 equal 21?​

Answers

9 + 10 does not equal 21.

If you add 9 and 10, you will get 19.

If you are referring to the meme, ok.

The required, left side of the expression 9 + 10 does not equal the right side expression 21.

The correct sum of 9 + 10 is 19. The statement "9 + 10 equals 21" is given by:
Consider the left side of the expression:
= 9 + 10
= 19

Where the right-hand side of the expression is 21, which implies
The left-hand side is not equal to the right-hand side.

However, mathematically, the sum is indeed 19.

Learn more about expression here:

https://brainly.com/question/31166009

#SPJ6

What is the area of the rectangle?

Answers

Answer:

c. 15cm^2

Step-by-step explanation:

Answer:

c. 15 cm

Step-by-step explanation:

Area is multiplication of height and length, (or whatever you call it) and 5 multiplied by 3=15

The volume of this cube is 1 ft. What is its surface area? A 6 ft. B 1 ft? C 26 ft? D 10 ft?​

Answers

Answer:

A

Step-by-step explanation:

The surface area of the cube is 6 ft².

What is a cube?

It is a polygon having six faces.

The volume of a cube is side³.

We have,

Volume = 1 ft³

The surface area of the cube = 6a²

Now,

Volume = 1 ft³

This means,

Side = 1 ft

a = 1 ft

So,

The surface area of the cube.

= 6a²

= 6 x 1²

= 6 ft²

Thus,

The surface area of the cube is 6 ft².

Learn more about cubes here:

https://brainly.com/question/11168779

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Part B
Jose predicts that the value of his car will decrease exponentially by 25% over the next 4 years. If Jose's prediction
is correct, about how much will his car be valued at, to the nearest thousand dollars, after 4 more years?

Answers

It will be more than 2,000 dollars

Which of the following is a composite number between 1 and 10? A. 5 B. 3 C. 7 D. 4

Answers

Answer:

b

Step-by-step explanation:

Answer:

Answer is D.

Step-by-step explanation:

I hope it's helpful!

9(1 + w) – 5w = 5
W=

Answers

Answer:

w= -1

Step-by-step explanation:

Use PEMDAS to solve.

9(1 + w) - 5w = 5

distribute 9 to everything inside the parentheses.

9 x 1 = 9

9 x w = 9w

rewrite equation

9 + 9w - 5w = 5

combine like terms

9w - 5w = 4w

rewrite equation

9 + 4w = 5

subtract 9 from both sides

9 - 9 = 0

5 - 9 = -4

rewrite equation

4w = -4

divide by 4 on both sides to get w by itself.

4w / 4 = w

-4 / 4 = -1

Hope This Helps :)

PLEASE HELP true or false I WILL MAKE BRAINLIEST

Answers

Answer:

True

Step-by-step explanation:

They are the same dimensions

Answer:

I think its true because there both the same shape and dimension

IS THE ANSWER B JUST TRYING TO CHECK

Answers

Answer:

No my dude its c

Step-by-step explanation:

Solve m1 and m2 In the diagram

Please help me solve Im so confused

Answers

Answer:

m<1=117

m<2=99

Step-by-step explanation:

Answer:

Angle 1 is 117 degrees.

Angle 2 is 59 degrees.

Step-by-step explanation:

Let angle 1 be x, and angle 2 be y.

By the exterior angle theorem, x + 21 = 138, so x = 138 - 21 = 117.

Again, by the exterior angle theorem, 79 + y = x = 138, so y = 138 - 79 = 59.

solve for X
(4x+7)
(2x+5)​

Answers

Answer:

x= 28

Step-by-step explanation:

combine the equations and set equal to 180, since a striaght line is 180 degrees. When combined you get, 6x + 12=180. Subtract, 180-12=168, then divide by 6 to get 28

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Answers

Answer:

...

Step-by-step explanation:

Answer:

Ok

Step-by-step explanation:

lolahsusnakaijaahasjssn

The equation of a function is
y = 12x - 7. What is the output when the input is 5?

A. 50
B. 53
C. 56
D. 60

Answers

the answer is B. 53
12 times 5 then sub 7
hope it helps
the answer is D
hope this helped

an object has a mass of 3 g and a volume of 4 ml, what is it's density?​

Answers

Answer:

Step-by-step explanation:

Density is mass divided  by volume

d = 3/4 = 0.75 g/mL

Step-by-step explanation:

density=mass/volume=3/4 g/ml

Twice a number is 17




Write it as an equation

Answers

The answer would be
~2*x=17~

Hope this helps

Have a great day/night

pls help me for 100 points!

Answers

Answer:

160

Step-by-step explanation:

Answer: 160

Step-by-step explanation:

A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the results of the survey. Freshmen Majors Major Number of Freshmen English 50 Science 35 Engineering 40 Business 45 Education 60 Undecided 50 Other 20 Which inference about all freshmen at this college is best supported by this information?​

Answers

Answer: The number of freshman who chose education as their major is greater than the number of freshman who chose science or other as their major ANSWER- D

Step-by-step explanation:

Answer:

Step-by-step explanation:

You drinking soda while playing a video game. You drank 4 full drinks over 3 1/3 rounds. If you drank the same amount each round, how much did you drink each round?

Answers

The answer to your problem would be 1 1/5 of the drink per round.

When asked about their favorite
holiday, only 10% of the class picked
Valentines Day. How many student
picked Valentine's Day if there were 30
students?

Answers

i think 27 but i thought it would have been 3 but that wouldn’t make sense so 27 ig

Please show your work in the answers. Please answer the 3 questions I put.

There are 30 pieces of candy in a bowl and 6 of them are Twix. What percentage of pieces of candy in the bowl are Twix?

Select the trip that will take 3 hours.
a. A train goes 60 miles per hour between Springfield and Boston, which is 180 miles away.
b. You bike to McDonald's at 10 miles per hour, which is 5 miles away.
c. You drive 80 miles per hour to New York City, which is 320 miles away.

A bird flies 40 miles, but it has only completed 80% of its trip. How far was the trip?​

Answers

Answer:

20%

a) a train goes 60 mph for 180 miles

50 miles

Step-by-step explanation:

6/30=.20 = 20%

180 miles divided by 60 mph=3 hours

80%x = 40 miles

.8x=40

.8x/.8=40/.8

x=50 miles

Which of the following are rays shown in the drawing?
BE
AC
AB
DC

Answers

Answer:

what drawing

Step-by-step explanation:

(-5y^2-9y-4)-(-2y^2-y+8)

Answers

Answer:

−3y2−8y−12

Step-by-step explanation:

Let's simplify step-by-step.

−5y2−9y−4−(−2y2−y+8)

Distribute the Negative Sign:

=−5y2−9y−4+−1(−2y2−y+8)

=−5y2+−9y+−4+−1(−2y2)+−1(−y)+(−1)(8)

=−5y2+−9y+−4+2y2+y+−8

Combine Like Terms:

=−5y2+−9y+−4+2y2+y+−8

=(−5y2+2y2)+(−9y+y)+(−4+−8)

=−3y2+−8y+−12

Answer:

[tex]-3y^2-8y-12[/tex]

Step-by-step explanation:

Simplify each term.

[tex]-5y^2-9y-4+2y^2+y-8[/tex]

Simplify by adding terms.

[tex]-3y^2-8y-12[/tex]

hope this helps :)

find the value of x ! geometry

Answers

Answer:

42.25485 or 42.25

Btw is this your homework or a test.

4. The costs of different sizes of bottled sport drink are shown. Which bottle costs the least per ounce?
Size
8 oz
16 oz
24 oz
32 oz
Price
$0.89
$1.09
$1.89
$2.39
A. The 8 oz bottle
B. The 16 oz bottle
C. The 24 oz bottle
D. The 32 oz bottle

Answers

I think it is the 16 oz bottle because it is only 6.8 cents per oz but I’m not positive sorry for not helping that much

A large can is 12 inches high the radius of the top is 3.5 inches what is the area of a rectangular label that is wrapped around the can

Answers

Answer:

the aria is what you need to multiply together

Step-by-step explanation:

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