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Dmitry_Shevchenko [17]
3 years ago
11

Y = X - 4 Linear Nonlinear

Mathematics
1 answer:
KengaRu [80]3 years ago
8 0

Answer:

Linear

Step-by-step explanation:

There is a constant rate of change ( 1 ), and there is a y-intercept.

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A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the
hichkok12 [17]

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%

8 0
3 years ago
Which expression is equivalent to sec²x - 1? A. cot²x B. tan²x C. CsC²x D. cos²x​
Andrei [34K]

Hi

Answer:

Step-by-step explanation:

3 0
2 years ago
What is the slope of the line that passes through the points (-2, 3)(−2,3) and (-14, -5) ?(−14,−5)? Write your answer in simples
NNADVOKAT [17]
I don't know the answer I'm just answering some thing so that Brinley will let me ask a question. Hope this helps LOL
7 0
2 years ago
7 gal 1 pt - 2 gal 7 pt =
Rus_ich [418]

Answer:

4 gal 2 pt

Step-by-step explanation:

8 pt = 1 gal

7 gal 1 pt = 57 pt

2 gal 7 pt = 23 pt

57 pt - 23 pt = 34 pt

34 pt = 4 gal 2 pt

5 0
3 years ago
Read 2 more answers
Please help with this, Thank You.
Dmitry [639]

Answer:

x = 12

Step-by-step explanation:

3x + 9 = 5x - 15

2x = 24

x = 12

4 0
2 years ago
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