Which of these represents an integer? a. -3 b. 4 c. 2 1/2 d. 6.2

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

what is the coeffcient of a term that consists of a single variable?For example,what is the coefficient of x

Viktor [21]

1 easy
x=1x

if you have a cow, how many do you have? 1

if ou have an x, how many do you have? 1

1 is coeficinet

6 0

3 years ago

Find the area of the shaded region.

Naily [24]

An.swer:

171.68

Step-by-step explanation:

6 0

3 years ago

A stone is thrown upward from ground level. With what minimum speed should the stone be thrown so as to reach a height of 49 fee

Sveta_85 [38]

The correct answer of the given question above would be 8ft/sec. The minimum speed that the stone be thrown so as to reach a height of 49 feet is 8ft/sec. Consider this given solution here:
u^2 = 2x a x 1
u^2 = 2 x 32 x 1 
u = 8 ft/sec
Hope this answer helps and this is what you are looking for.

6 0

4 years ago

PLEASE HELP AND HURRY

kogti [31]

Here the given expression is

$y =(\frac{3}{4})^x$

We need to find the value of y when x =3 . So we substitute the value of x in the given expression.

$y =(\frac{3}{4})^3 = \frac{27}{64} =0.4$

So when x=3, y=0.4 and that's the required answer.

6 0

3 years ago