How do you isolate the variable in an inequality?

If outliers are discarded, then the retirement savings by residents of Econistan is normally distributed with a mean of $100,000

zavuch27 [327]

Answer:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

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

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

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

$X \sim N(100000,20000)$

Where $\mu=100000$ and $\sigma=20000$

We are interested on this probability

$P(X>117000)$

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:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

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

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

7 0

3 years ago

How do i Solve: 3x2−6x−12=0 ?

MrMuchimi

Answer:

1 + root 5, 1 - root 5

Step-by-step explanation:

I assume you mean 3x^2-6x-12=0.

First, note that you can divide both sides by 3. You get:

x^2-2x-4=0

Use the quadratic equation.

$x=\frac{2\pm\sqrt{4+16}}{2}=\frac{2\pm2\sqrt{5}}{2}=1\pm\sqrt{5}$

Therefore, x=1 + root 5, 1 - root 5

4 0

3 years ago

Challenge You have 2 different savings accounts. For Account A, the simple interest earned after months is $. For Account B,

Debora [2.8K]

Answer and Step-by-step explanation:

The computation is shown below;

As we know that

The simple interest is

Simple interest = Principal × rate × time

For Account A, the principal would be

2 = Principal × 3.2% × 3

So, the principal is $20.83

For account B, the principal would be

38.50 = Principal × 2.2% × 30

So, the principal is $58.33

Now the interest for both the accounts are as follows

For account 1

= $20.83 × 3.2%

= $0.67

And, for the account 2

= $58.33 × 2.2%

= $1.28

As it can be seen that the account 2 has the highest interest

The same is to be considered

7 0

3 years ago

One of your employees is bidding on a carpet installation job. They estimate that it will take 3 hours to install 12 square yard

Charra [1.4K]

Answer:

No, the bid is not correct.

Step-by-step explanation:

One of your employees is bidding on a carpet installation job.

They estimate that it will take 3 hours to install 12 square yards of carpeting.

we know that 1 square yard= 9 square foot.

12 square yard= 12×9 square foot=108 square foot

i.e. it takes 3 hours to carpet 108 square foot.

Hence time taken to carpet 1 square foot= $\dfrac{3}{108}$ hour

Now the dimension of room is:

11' 6"× 12' 9" i.e. we convert both the units to foot as:

1 foot= 12 inch

11'6"=11+(6/12)=11.5 foot.

and 12'9"=12+(9/12)=12.75 foot.

Hence, dimension of room=11.5 foot×12.75 foot

Hence area of room=11.5×12.75=146.625 square foot.

Time to carpet 146.625 square foot=

$\dfrac{3}{108}\times 146.625$ hour

=4.0729 hour

But it is given that it takes 12.3 hours to install the carpet.

Hence, the calculations were wrong.

6 0

3 years ago

Read 2 more answers

I need help with 2-3

alekssr [168]

Answer:

1

Step-by-step explanation:

6 0

3 years ago