Hey! please help i’ll give brainliest!

The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of

Karo-lina-s [1.5K]

Answer:

a) $P(\bar X$

b) $P(98$

c) $P(\bar X$

d) $P(93$

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

$X \sim N(99.9,30)$

Where $\mu=99.9$ and $\sigma=30$

We select a random sample of n=36. And from the central limit theorem we know that the distribution for the sample is given by:

$\bar X \sim N(\mu =99.9 , \frac{\sigma}{\sqrt{n}}= \frac{30}{\sqrt{38}}=4.87)$

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

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

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

$P(\bar X$

$=P(Z$

Part b

For this case we want this probability:

$P(98$

$=P(\frac{98-99.9}{\frac{30}{\sqrt{38}}}$

And we can find this probability on this way:

$P(-0.39$

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

$P(-0.39$

Part c

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

$P(\bar X$

Part d

For this case we want this probability:

$P(93$

$=P(\frac{93-99.9}{\frac{30}{\sqrt{38}}}$

And we can find this probability on this way:

$P(-1.42$

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

$P(-1.42$

3 0

3 years ago

A plant manager needs 75 sq. yds. of fabric and the fabric is only 32 in. wide. How many linear feet must she make to produce 75

Svetllana [295]

Probably d because it's 23.45

8 0

3 years ago

Read 2 more answers

Dy/dx of ln(x/x^²+1)

exis [7]

$\dfrac{dy}{dx}\ \ln\left(\dfrac{x}{x^2+1}\right)=\dfrac{1}{\frac{x}{x^2+1}}\cdot\dfrac{x'(x^2+1)-x(x^2+1)'}{(x^2+1)^2}\\\\=\dfrac{x^2+1}{x}\cdot\dfrac{1(x^2+1)-x(2x)}{(x^2+1)^2}=\dfrac{1}{x}\cdot\dfrac{x^2+1-2x^2}{x^2+1}=\dfrac{1-x^2}{x^3+x}\\\\Used:\\\\(\ln(x))'=\dfrac{1}{x}\\\\\left[f(g(x))\right]'=f'(g(x))\cdot g'(x)\\\\\left(\dfrac{f(x)}{g(x)}\right)'=\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$

5 0

3 years ago

Give an example of each of the following or explain why you think such a set could not exist.

Oksanka [162]

Answer:

a.No

b.No

c.No

Step-by-step explanation:

a.No,Such set does not exist .A set of natural numbers is N

Every point of this set is an isolated point but no accumulation point

Accumulation point:It is defined as that point a of set Swhich every neighborhood contains infinitely many distinct point of set

$(a-\epsilon,e+\epsilon)\cap S-{a}\neq\phi$

Isolated point : it is defined as that point a of set S which neighborhood does not contain any other point of set except itself

$(a-\epsilon0,a+\epsilon)\cap S-{a}=\phi$

Interior point of set :Let $a\in S$ .Then a is called interior point of set when its neighborhood is a subset of set S.

$a\in(a-\epsilon,e+\epsilon)\subset S$

When a set is uncountable then interior point exist it is necessary for interior points existance .

Boundary points :Let $a\in S$ .If every non empty neighborhood of a intersect S and complement of S.

Every member of a set is a boundary point

b.No, such set does not exist .A non empty set with isolated point then the set have no interior points .By definition of interior point and isolated point .For example.set of natural numbers

c.No, Such set does not exist ,for example set of natural every point is an isolated point and boundary point.By definition of boundary point and isolated point

6 0

3 years ago

A car starts from an initial velocity of 10m/s and accelerates at 2.5m/s².how long will it take the car to reach a speed of 40m/

PIT_PIT [208]

A=(v-u)/t
We know a=2.5, v=40, u=10, so:
2.5=(40-10)/t
2.5t=40-10
2.5t=30
Divide both sides by 2.5
t=12 It takes 12 seconds for the car to reach 40m/s

To find out how far it went, you do:
d=v+1/2 at^2
d=10+1/2(2.5)(12)^2
d=10+1/2(2.5)(144)
d=10+(1.25)(72)
d=10+90
d=100m

Hope this helps :)

7 0

3 years ago