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Leno4ka [110]
3 years ago
8

I will give brainiest to whoever answers correctly !!

Mathematics
1 answer:
schepotkina [342]3 years ago
7 0

Answer:

12,000

Step-by-step explanation:

i believe this would be what she withdrew but if not i'm sorry for giving the wrong answer

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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 of the following could be the graph of the line y = 3x - 2?
morpeh [17]

You didn't give a graph but I will visualize what it looks like for you.

The line is going through (0,-2) because that is the y-intercept.

The line has a slope of 3.

So, the line goes through:

(1,1)

(2,4)

(3,7)

(4,10)

(5,13)

5 0
3 years ago
Read 2 more answers
The highest recorded temperature during the month of July for a given year in Death Valley, California has an approximately norm
S_A_V [24]

Answer:

P(X

And we can find this probability using excel or the normal standard tabe and we got:

P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:

X \sim N(123.8,3.1)  

Where \mu=123.8 and \sigma=3.1

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using excel or the normal standard tabe and we got:

P(z

6 0
3 years ago
What is the value of p in the equation 13p+42=-57+2p
ira [324]

Answer:

p=-9

Step-by-step explanation:

13p+42=-57+2p

Subtract 2p from each side

13p-2p+42=-57+2p-2p

11p +42 = -57

Subtract 42 from each side

11p+42-42=-57-42

11p = -99

Divide each side by 11

11p/11 = -99/11

p = -9

6 0
3 years ago
Which graph represents the solution to the inequality 3 < 2- x/3 <7/2
Tems11 [23]

Answer:

C

Step-by-step explanation:

3 0
3 years ago
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