1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Serjik [45]
3 years ago
11

The average number of annual trips per family to amusement parks in the UnitedStates is Poisson distributed, with a mean of 0.6

trips per year. What is the probabilityof randomly selecting an American family and finding the following?a.The family did not make a trip to an amusement park last year.b.The family took exactly one trip to an amusement park last year.c.The family took two or more trips to amusement parks last year.d.The family took three or fewer trips to amusement parks over a three-year period.e.The family took exactly four trips to amusement parks during a six-year period.
Mathematics
1 answer:
IrinaK [193]3 years ago
4 0

Answer:

a) 0.5488 = 54.88% probability that the family did not make a trip to an amusement park last year.

b) 0.3293 = 32.93% probability that the family took exactly one trip to an amusement park last year.

c) 0.1219 = 12.19% probability that the family took two or more trips to amusement parks last year.

d) 0.8913 = 89.13% probability that the family took three or fewer trips to amusement parks over a three-year period.

e) 0.1912 = 19.12% probability that the family took exactly four trips to amusement parks during a six-year 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 distributed, with a mean of 0.6 trips per year

This means that \mu = 0.6n, in which n is the number of years.

a.The family did not make a trip to an amusement park last year.

This is P(X = 0) when n = 1, so \mu = 0.6.

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

P(X = 0) = \frac{e^{-0.6}*(0.6)^{0}}{(0)!} = 0.5488

0.5488 = 54.88% probability that the family did not make a trip to an amusement park last year.

b.The family took exactly one trip to an amusement park last year.

This is P(X = 1) when n = 1, so \mu = 0.6.

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

P(X = 1) = \frac{e^{-0.6}*(0.6)^{1}}{(1)!} = 0.3293

0.3293 = 32.93% probability that the family took exactly one trip to an amusement park last year.

c.The family took two or more trips to amusement parks last year.

Either the family took less than two trips, or it took two or more trips. So

P(X < 2) + P(X \geq 2) = 1

We want

P(X \geq 2) = 1 - P(X < 2)

In which

P(X < 2) = P(X = 0) + P(X = 1) = 0.5488 + 0.3293 = 0.8781

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.8781 = 0.1219

0.1219 = 12.19% probability that the family took two or more trips to amusement parks last year.

d.The family took three or fewer trips to amusement parks over a three-year period.

Three years, so \mu = 0.6(3) = 1.8.

This is

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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

P(X = 0) = \frac{e^{-1.8}*(1.8)^{0}}{(0)!} = 0.1653

P(X = 1) = \frac{e^{-1.8}*(1.8)^{1}}{(1)!} = 0.2975

P(X = 2) = \frac{e^{-1.8}*(1.8)^{2}}{(2)!} = 0.2678

P(X = 3) = \frac{e^{-1.8}*(1.8)^{3}}{(3)!} = 0.1607

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1653 + 0.2975 + 0.2678 + 0.1607 = 0.8913

0.8913 = 89.13% probability that the family took three or fewer trips to amusement parks over a three-year period.

e.The family took exactly four trips to amusement parks during a six-year period.

Six years, so \mu = 0.6(6) = 3.6.

This is P(X = 4). So

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

P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.1912

0.1912 = 19.12% probability that the family took exactly four trips to amusement parks during a six-year period.

You might be interested in
Check if 7 is a solution of the equation 4 ( Z - 3 ) = 16. step by step plz guys. ​
Vilka [71]

Answer:

YES

Step-by-step explanation:

4(Z-3)=16

4Z-12=16

  +12 +12

4Z=28

Z=7

3 0
2 years ago
Read 2 more answers
The abc store sold 142 c.d.'s at $10.50 each, 80 audio tapes which cost $8.00 a price, 30 videos priced at $15.00 each and $150
Lina20 [59]

Answer:

2731

Step-by-step explanation:

Mark me brainiest

7 0
3 years ago
What is the side length a in the triangle below?
grigory [225]

Answer:

a=5

Step-by-step explanation:

a^2+b^2=c^2

c^2-b^2=a^2

13^2-12^2=a^2

169-144=a^2

25=a^2

5=a

8 0
2 years ago
Find the product:<br> (-9)(-4)
nadya68 [22]

Answer:

36

Step-by-step explanation:

-9*-4=36

3 0
3 years ago
Henry can write 5 1/4 pages of his novel in 3 hours how many page can he write in 8 hours
ICE Princess25 [194]
If you would like to know how many pages can Henry write in 8 hours, you can calculate this using the following steps:

5 1/4 = 21/4 pages ... 3 hours
x pages = ? ... 8 hours

21/4 * 8 = 3 * x
21 * 2 = 3 * x
3 * x = 42
x = 42 / 3
x = 14 pages

Henry can write 14 pages of his novel in 8 hours.
8 0
3 years ago
Other questions:
  • From 100 yards away, a marksman hit 16/23 of the targets last year. Rewrite the fraction as a percentage.
    10·1 answer
  • Help me please please please
    9·1 answer
  • Determine dy/dx in terms of t and evaluate it at the given value of t for the following parametric curves.a. x = 3 sin t, y = 2
    10·1 answer
  • Which is a rational number?<br> √6<br> √36/16<br> √16/6<br> √36/6
    7·1 answer
  • HELP ME WITH THIS PLEASE!!!!!
    11·2 answers
  • If Triangle J K L is congruent to Triangle B C A, which statement must be true?
    8·2 answers
  • Write an equation in simplest form that can be used to find the value of x. (Don’t find the value of x)
    6·1 answer
  • Help please!<br>figure out the "inflection point" of the following function<br>f(x)=5x³ + 2x² − 3x​
    10·2 answers
  • Which of the following is not a recommendation the author of the Businesstown.com article makes to lower your
    11·2 answers
  • PLSS HELP ME CUS YES
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!