If f(x) = 2x – 1 and g(x) = ^ – 2, find [g ◦ f](x).

Consider a sampling distribution with p equals 0.15p=0.15 and samples of size n each. Using the appropriate formulas, find the

Grace [21]

Answer:

$a.\ \mu_p=750\ \ , \sigma_p=0.005\\\\b.\ \mu_p=150\ \ , \sigma_p=0.0113\\\\c.\ \mu_p=75\ \ , \sigma_p=0.0160$

Step-by-step explanation:

a. Given p=0.15.

-The mean of a sampling proportion of n=5000 is calculated as:

$\mu_p=np\\\\=0.15\times 5000\\\\=750$

-The standard deviation is calculated using the formula:

$\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.15(1-0.15)}{5000}}\\\\=0.0050$

Hence, the sample mean is μ=750 and standard deviation is σ=0.0050

b. Given that p=0.15 and n=1000

#The mean of a sampling proportion of n=1000 is calculated as:

$\mu_p=np\\\\=1000\times 0.15\\\\\\=150$

#-The standard deviation is calculated as follows:

$\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{1000}}\\\\\\=0.0113$

Hence, the sample mean is μ=150 and standard deviation is σ=0.0113

c. For p=0.15 and n=500

#The mean is calculated as follows:

$\mu_p=np\\\\\\=0.15\times 500\\\\=75$

#The standard deviation of the sample proportion is calculated as:

$\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{500}}\\\\\\=0.0160$

Hence, the sample mean is μ=75 and standard deviation is σ=0.0160

4 0

3 years ago

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today

Ierofanga [76]

Answer:

a) We can find the z score for the value of 225 and we got:

$z = \frac{225-204}{55}=0.382$

And we can find this probability with the complement rule:

$P(z>0.382)=1-P(z$

b) $z = \frac{140-204}{55}=-1.164$

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

$P(z$

c) $P(200$

And we can find this probability with this difference:

$P(-0.072$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.072$

d) For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.2$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.8 of the area on the left and 0.2 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.2

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.842$

And if we solve for a we got

$a=204 +0.842*55=250.31$

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".

Part a

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

$X \sim N(204,55)$

Where $\mu=204$ and $\sigma=55$

We are interested on this probability

$P(X>225)$

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

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

We can find the z score for the value of 225 and we got:

$z = \frac{225-204}{55}=0.382$

And we can find this probability with the complement rule:

$P(z>0.382)=1-P(z$

Part b

$P(X$

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:

$z = \frac{140-204}{55}=-1.164$

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

$P(z$

Part c

$P(200$

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:

$P(200$

And we can find this probability with this difference:

$P(-0.072$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.072$

Part d

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.2$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.8 of the area on the left and 0.2 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.2

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.842$

And if we solve for a we got

$a=204 +0.842*55=250.31$

5 0

3 years ago

. What is 60% of 52?<br> SHOW WORK:

Bess [88]

Answer:

32.1% ( depending on question might have to round to 32% )

Step-by-step explanation:

60*52=3210

3210/100= 32.1

6 0

3 years ago

Read 2 more answers

Use point slope form to write the lines with the given slope and point in slope intercept form.m= -1(-5,-4)

lara31 [8.8K]

The slope point form is

$y-y1=m(x-x1)$

m is the slope

x1, y1 are the coordinates of a point on the line

The slope of the line is -1

m = -1

point (-5, -4) lies on the line

x1 = -5 and y1 = -4

Let us substitute them in the form above

$y-(-4)=-1(x-\lbrack-5\rbrack)$

Remember (-)(-) = (+)

$y+4=-1(x+5)$

The equation of the line in the slope-point form is y + 4 = -1(x + 5)

6 0

1 year ago

If f(x) = -2x - 3, find f(0) - 7. <br><br><br>help please!! I will give brainliest!!!!

VikaD [51]

Hi there!

$\huge\boxed{-10}$

f(x) = -2x - 3

Plug in 0 for "x" to solve for f(0):

f(0) = -2(0) - 3

f(0) = -3

Since the question is asking you to evaluate f(0) - 7, simply subtract:

-3 - 7 = -10.

7 0

2 years ago