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
kow [346]
3 years ago
12

25% of American households have only dogs (one or more dogs) 15% of American households have only cats (one or more cats) 10% of

American households have dogs and cats (one or more of each) 50% of American households do not have any dogs or cats. A researcher randomly samples 10 American households. Find the probability that exactly 3 have only dogs, 2 has only cats, 1 has cats and dogs, and 4 has neither cats or dogs. Round your answer to 4 decimal places.
Mathematics
1 answer:
sergeinik [125]3 years ago
8 0

Answer:

a) P=0.2503

b) P=0.2759

c) P=0.3874

d) P=0.2051

Step-by-step explanation:

We have this information:

25% of American households have only dogs (one or more dogs)

15% of American households have only cats (one or more cats)

10% of American households have dogs and cats (one or more of each)

50% of American households do not have any dogs or cats.

The sample is n=10

a) Probability that exactly 3 have only dogs (p=0.25)

P(x=3)=\binom{10}{3}0.25^30.75^7=120*0.01563*0.13348=0.25028

b) Probability that exactly 2 has only cats (p=0.15)

P(x=2)=\binom{10}{2}0.15^20.85^8=45*0.0225*0.27249=0.2759

c) Probability that exactly 1 has cats and dogs (p=0.1)

P(x=1)=\binom{10}{1}0.10^10.90^0=10*0.1*0.38742=0.38742

d) Probability that exactly 4 has neither cats or dogs (p=0.5)

P(x=4)=\binom{10}{4}0.50^40.50^6=210*0.0625*0.01563=0.20508

You might be interested in
What's the best Approximation? :3
musickatia [10]
Area of shaded region = Area of larger circle - Area of smaller circle.

We know, Area of a Circle = πr²
So, A = πr₁² - πr₂²
A = π (r₁² - r₂²)
A = π(10.2² - 5.4²)
A = 3.14 (104.04 - 29.16)
A = 3.14 (74.88)
A = 235.12

In short, Your Answer would be 235.12 cm²

Hope this helps!
3 0
3 years ago
Carol buys a house for £234 900
Aneli [31]

Answer:

23,490

Step-by-step explanation:

10% = 0.1

234900 x 0.1 = 23490

3 0
3 years ago
Read and choose the correct words for the blank that match the image. (1 point) A cook using pepper on food cooking in a pan Me
spayn [35]

Answer:

C) la pimienta

Step-by-step explanation:

8 0
2 years ago
Simplify the following 18x^4-9x^2+12x/3x^2
Crank

I think its x^2(18x^2 -9+4x) sorry if I’m wrong

5 0
3 years ago
Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi
Leokris [45]

Answer:

If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

Sample size, n = 8

Sample:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

s = \sqrt{\dfrac{875.5}{7}} = 11.18

\text{ Sample variance} = s^2 = 125.07

Population:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46

\text{ Population variance} = \sigma^2 = 109.44

7 0
3 years ago
Other questions:
  • The real number square root over 23 belongs to which set of numbers? irrational numbers integers rational numbers whole numbers
    10·1 answer
  • Which transformation will map figure K onto figure K'? Two congruent kites figure K and figure K prime are drawn on a coordinate
    11·1 answer
  • Find the first ten prime numbers tell how you do it
    15·2 answers
  • Solve the system of equations: y= 3x y= x^2 - 4
    11·1 answer
  • Internet prices for glasses are often considerably lower than those at the brick and mortar stores but quality is another questi
    15·1 answer
  • In the triangle below, x= degree. Round to the nearest tenth
    15·1 answer
  • Use the distributive property to multiply 3(-2m+1)​
    13·1 answer
  • Anybody have a clue ?
    12·2 answers
  • Can you please help me with this question
    15·1 answer
  • The library has 28 science fiction books. Each shelf holds 5 books,
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!