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
dolphi86 [110]
3 years ago
8

A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the

proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
Mathematics
1 answer:
hichkok12 [17]3 years ago
8 0

Answer:

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

A statistician calculates that 8% of Americans own a Rolls Royce.

This means that p = 0.08

Sample of 595:

This means that n = 595

Mean and standard deviation:

\mu = p = 0.08

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111

What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?

Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.

Probability the proportion is less than 5%:

P-value of Z when X = 0.05. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.05 - 0.08}{0.0111}

Z = -2.7

Z = -2.7 has a p-value of 0.0035

2*0.0035 = 0.0070

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

You might be interested in
Secθ =__________________<br><br> 1/sinθ<br><br> +-√cos^2 +1<br><br> +-√tan^2 +1
Zielflug [23.3K]

Answer:

The answer is last option

As we know 1 + tan^2 = sec^2

6 0
3 years ago
Read 2 more answers
Suppose f(x) is a function which satisfies f'(3) = 0,f'(5) = 0, f"(3) = -4, and f"(5) = 5.
Dennis_Churaev [7]
If you find the answer let me know please e
8 0
2 years ago
Marking brianliest pls help
Contact [7]

Answer:

117.3

Step-by-step explanation:

7*4=117.29=117.3

6 0
2 years ago
<img src="https://tex.z-dn.net/?f=211%3D6%283%2B8x%29%2B1" id="TexFormula1" title="211=6(3+8x)+1" alt="211=6(3+8x)+1" align="abs
harkovskaia [24]
X=4
211=18+48x+1
211=19+48x
5 0
3 years ago
Read 2 more answers
Consider H0: μ = 45 versus H1: μ &lt; 45. A random sample of 25 observations produced a sample mean of 41.8. Using α = .025 and
a_sh-v [17]
Given
H0: \ \mu=45 \\  \\ H1: \ \mu\ \textless \ 45
This is a one-tailed test.

z= \frac{41.8-45}{6/ \sqrt{25} } = \frac{-3.2}{6/5} = \frac{-3.2}{1.2} =-2.6667

P(z\ \textless \ -2.6667)=0.00383

Since the p-value of the sample statistic (0.00383) is less that the significant level (0.025), we reject the null hypothesis.
5 0
3 years ago
Other questions:
  • Suppose that 5 identical red wooden blocks and 6 identical white wooden blocks are to be​ stacked, one on top of​ another, to fo
    11·2 answers
  • Sarah has completed the first few steps for constructing the inscribed circle for triangle ABC. She started by constructing the
    13·2 answers
  • WILL MARK BRAINLIEST! PLEASE HELP MEH!Use the relationship between the angles in the figure to answer the question. Which equati
    12·2 answers
  • My finals are tomorrow and i need to sleep soon, any answer would be appreciated, and i REALLY REALLY need explanations with the
    11·2 answers
  • Write the number 0.00003852 in standard form
    7·1 answer
  • Use the basic probability principle to solve the following problem. Express each probability as a fraction reduced to lowest ter
    13·1 answer
  • Solve e^x = e^2x + 5.
    12·1 answer
  • I have to select all the expressions that are equivalent to the factored form of: 36a-16. the answers are 4(9a-4), 2(18a-8), 6(6
    5·1 answer
  • My brother took the car to the airport to pick up family members. The rate that the car was traveling was measured in miles to h
    14·1 answer
  • Match each expression with its value.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!