The original price of a dining table set is $400. The set is on sale for 40% off. What is the sale price of the set?

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a

zaharov [31]

Answer:

a) $P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)$

And we can find this probability using the complement rule:

$P(z>-1.25)=1-P(z$

b) $P(X$

And we can find this probability uing the normal standard table:

$P(z$

c) $P(3.5$

And we can find this probability with this difference:

$P(-1.25$

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

$P(-1.25$

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 variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(5,1.2)$

Where $\mu=5$ and $\sigma=1.2$

We are interested on this probability

$P(X>3.5)$

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:

$P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)$

And we can find this probability using the complement rule:

$P(z>-1.25)=1-P(z$

Part b

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 uing the normal standard table:

$P(z$

Part c

$P(3.5$

And we can find this probability with this difference:

$P(-1.25$

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

$P(-1.25$

3 0

3 years ago

Identify the slope y-intercept of the function y= -2x + 3.

Anna11 [10]

Answer:

First option.

Step-by-step explanation:

Use the formula y = mx + b.

Where m is the slope, and b is the y-intercept.

y = -2x + 3

The slope is -2. The y-intercept is (0, 3).

5 0

3 years ago

In algebra, we often study relationships where a change to one variable causes change in another variable. Describe a situation

vampirchik [111]

Answer:

A familiar situation is: cost of books you pay for versus the quantity of books bought.

Cost of books ($) and quantity of books are directly proportionally related in the situation.

The graph will look like the graph in the attachment below.

A quantity (dependent variable) will change constantly in relation to another quantity (independent variable) if the relation is a proportional relationship.

A familiar situation for example can be the cost you pay for books will be directly proportional or dependent on the number of books you bought.

That is:

Number of books = independent variable

Cost ($) = dependent variable

A change in the number of books will cause a change in the cost you will pay for buying books.

This shows a direct proportional relationship between the two quantities.

On a straight line graph, the graph will be a proportional graph showing number of books on the x-axis against cost ($) you pay on the y-axis.

Therefore:

A familiar situation is: cost of books you pay for versus the quantity of books bought.

Cost of books ($) and quantity of books are directly proportionally related in the situation.

Step-by-step explanation:

hope this helps cutey ;)

3 0

3 years ago

Can someone plz help me with this one problem plz!!!

Lady bird [3.3K]

2,14 4,16 6,18 8,20 f=s+12

4 0

3 years ago

16) Please help with question. WILL MARK BRAINLIEST + 10 POINTS.

Katyanochek1 [597]

We will use the sine and cosine of the sum of two angles, the sine and consine of $\frac{\pi}{2}$ , and the relation of the tangent with the sine and cosine:

$\sin (\alpha+\beta)=\sin \alpha\cdot\cos\beta + \cos\alpha\cdot\sin\beta

\cos(\alpha+\beta)=\cos\alpha\cdot\cos\beta-\sin\alpha\cdot\sin\beta$

$\sin\dfrac{\pi}{2}=1,\ \cos\dfrac{\pi}{2}=0$

$\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha}$

If you use those identities, for $\alpha=x,\ \beta=\dfrac{\pi}{2}$ , you get:

$\sin\left(x+\dfrac{\pi}{2}\right) = \sin x\cdot\cos\dfrac{\pi}{2} + \cos x\cdot\sin\dfrac{\pi}{2} = \sin x\cdot0 + \cos x \cdot 1 = \cos x$

$\cos\left(x+\dfrac{\pi}{2}\right) = \cos x \cdot \cos\dfrac{\pi}{2} - \sin x\cdot\sin\dfrac{\pi}{2} = \cos x \cdot 0 - \sin x \cdot 1 = -\sin x$

Hence:

$\tan \left(x+\dfrac{\pi}{2}\right) = \dfrac{\sin\left(x+\dfrac{\pi}{2}\right)}{\cos\left(x+\dfrac{\pi}{2}\right)} = \dfrac{\cos x}{-\sin x} = -\cot x$

3 0

3 years ago

The original price of a dining table set is $400. The set is on sale for 40% off. What is the sale price of the set?​

The original price of a dining table set is $400. The set is on sale for 40% off. What is the sale price of the set?