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
Free_Kalibri [48]
3 years ago
10

It's all politics: A politician in a close election race claims that 52% of the voters support him. A poll is taken in which 200

voters are sampled, and 44% of them support the politician.
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
3 0

Answer:

a) P(x ≤ 0.44) = 0.02275

b) The probability of obtaining a sample proportion less than or equal to 0.44 is very low (2.275%), hence, it would be unusual to obtain a sample proportion less than or equal to 0.44.

c) P(x ≤ 0.50) = 0.30854

A probability of 30.854% doesn't scream unusual, but it is still not a very high probability. So, it is still slightly unusual to obtain a sample proportion of less than half of the voters that don't support the politician.

Step-by-step explanation:

Given,

p = population proportion that support the politician = 0.52

n = sample size = 200

(np = 104) and [np(1-p) = 49.92] are both greater than 10, So, we can treat this problem like a normal distribution problem.

This is a normal distribution problem with

Mean = μ = 0.52

Standard deviation of the sample proportion in the distribution of sample means = σ = √[p(1-p)/n]

σ = √[0.52×0.48)/200]

σ = 0.035 ≈ 0.04

a) Probability of obtaining a sample proportion that is less than or equal to 0.44. P(x ≤ 0.44)

We first normalize/standardize/obtain z-scores for a sample proportion of 0.44

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (0.44 - 0.52)/0.04 = -2.00

To determine the probability of obtaining a sample proportion that is less than or equal to 0.44.

P(x ≤ 0.44) = P(z ≤ -2)

We'll use data from the normal probability table for these probabilities

P(x ≤ 0.44) = P(z ≤ -2) = 0.02275

b) Would it be unusual to obtain a sample proportion less than or equal to 0.44 if the politician's claim is true?

The probability of obtaining a sample proportion less than or equal to 0.44 is 0.02275; that is, 2.275%.

The probability of this occurring is very low, hence, it would be unusual to obtain a sample proportion less than or equal to 0.44.

c) If the claim is true, would it be unusual for less than half of the voters in the sample to support the politician?

Sample proportion that matches half of the voters = 0.50

P(x < 0.50)

We follow the same pattern as in (a)

We first normalize/standardize/obtain z-scores for a sample proportion of 0.50

z = (x - μ)/σ = (0.50 - 0.52)/0.04 = -0.50

To determine the probability of obtaining a sample proportion that is less than 0.50

P(x < 0.50) = P(z < -0.50)

We'll use data from the normal probability table for these probabilities

P(x < 0.50) = P(z < -0.50) = 1 - P(z ≥ -0.50) = 1 - P(z ≤ 0.50) = 1 - 0.69146 = 0.30854

Probability of obtaining a sample proportion of less than half of the voters that support the politician = 0.30854 = 30.854%

This value is still not very high, it would still he unusual to obtain such a sample proportion that don't support the politician, but it isn't as unusual as that calculated in (a) and (b) above.

Hope this Helps!!!

You might be interested in
Jude estimates that his index finger is 3 inches long. He calculates the circumference of one of his bongo drums to be 27 inches
anzhelika [568]

Answer: 9 finger lengths

Step-by-step explanation: Since the circumference is the middle line passing through (usually a circle....) 27/3 equals 9, which basically means that 9 of Jude's index fingers can pass through the circumference of one of his bongo drums. Hope this helps, 15402256.

7 0
3 years ago
For a bake sale, Trisha wants to make between 144 and 168 cookies. She already has 24 cookies made and has 4 hours left to bake
mafiozo [28]
She sold 57 cookies 57 will be the awnser
5 0
3 years ago
6) Find the difference of (4x - 5) and (6x + 8)
Allushta [10]

Answer:

-2x- 13

Step-by-step explanation:

Hi there!

(4x - 5)-(6x + 8)

Open up the parentheses

4x - 5-6x - 8

Combine like terms

4x -6x- 5 - 8\\-2x- 13

I hope this helps!

6 0
3 years ago
Read 2 more answers
The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 &lt; T &lt; 36 , where T is
antoniya [11.8K]

Answer:

N(T(t)) = 1408t^2 - 385.6t - 105.52

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

N(T(t)) = 22 * (8t + 1.7)^2  - 123 * (8t + 1.7) + 40

N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40

N(T(t)) = 1408t^2 + 598.4t + 63.58 -  984t - 169.1

N(T(t)) = 1408t^2 - 385.6t - 105.52

Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

8019 = 1408t^2 - 385.6t - 105.52

1408t^2 - 385.6t - 8124.52 = 0

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

4 0
3 years ago
No sé cómo hacerlo. Y me gustaría que me ayudaran con él proceso?
In-s [12.5K]

Answer:

BC=11

Step-by-step explanation:

we need to find BC

and we  know that

AB= x+2

AC=13

BC=2x+11

A, B and C are collinear

that means that

AB+BC=AC

x+2+2x+11=13

3x+13=13

3x=0

x=0

so BC=2(0)+11

BC=11

7 0
2 years ago
Other questions:
  • The sales tax on the purchase of a futon is ​$24.45. If the tax rate is 5​%, find the purchase price of the futon
    6·2 answers
  • 8. A well-balanced stock market portfolio will often experience an exponential growth. A
    15·1 answer
  • What is the area of the triangle below?
    14·1 answer
  • What is 0.6 equal to as a fraction
    15·2 answers
  • What would be the expression?
    15·1 answer
  • If the sin of angle x is 4 over 5 and the triangle was dilated to be two times as big as the original, what would be the value o
    15·1 answer
  • The slope of the tangent to the curve y^3x + y^2x^2 = 6 at (2,1)
    5·1 answer
  • Plz help asap help will appreiciated
    6·1 answer
  • I don't understand help plz​
    13·2 answers
  • Ind the approximate increase in its area if its radius increases from mm to mm.​ [Recall that the area of a circle is A​.]
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!