Which could be the name of a line?

Mathematics

1 answer:

Andrei [34K]3 years ago

6 0

Maybe the answer is B but im not sure

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Out of 2,000 random but normally distributed numbers with a mean of 45 and a standard deviation of x, approximately 1,360 number

Lilit [14]

Let $Y$ denote the random variable representing a given number in the total set of numbers. We're told that $\dfrac{1360}{2000}=0.68$ of the numbers fall within a given range, so we know

$\mathbb P(40\le Y\le50)=0.68$

where $Y$ is normally distributed with mean 45 and an unknown variance $x^2$ .

Let's make the transformation to a random variable with a standard normal distribution:

$\mathbb P\left(\dfrac{40-45}x\le\dfrac{Y-45}x\le\dfrac{50-45}x\right)=\mathbb P\left(-\dfrac5x\le Z\le\dfrac5x\right)$

Since $Z$ is symmetric, we have

$\mathbb P(-\dfrac5x\le Z\le\dfrac5x\right)=2\mathbb P\left(0\le Z\le\dfrac5x\right)=2\bigg(\mathbb P\left(Z\le\dfrac5x\right)-\mathbb P(Z\le0)\bigg)$

The mean of $Z$ is 0, and by symmetry we know that exactly half of the distribution falls to the left of $Z=0$ , so $\mathbb P(Z\le0)=0.5$ . We're left with

$0.68=2\mathbb P\left(Z\le\dfrac5x\right)-2\cdot0.5$
$\implies\mathbb P\left(Z\le\dfrac5x\right)=0.84$

This probability corresponds to a value of $Z\approx0.9945$ , which means

$\dfrac5x\approx0.9945\implies x\approx5.0277$

7 0

3 years ago

Can anyone teach me how to calculate this surface area ?

Firlakuza [10]

Answer:

Step-by-step explanation:

oof. okay.

so basically you have to find the area of each face of this shape

so I will write each area for you just so that I can keep track of where I am.

So the top one is 2*3=6

and then the side of that is 3*1=3

and then the next stair is 3*1 =3

and then again another 3*1=3

and the top of the bottom stair is 3*1=3

the side of that last one is 2*3=6

the back of the stair thingy is 4*3=12

now the weird side is (4*2)+(3*1)+(2*1)=13

you need two of those sides so another (4*2)+(3*1)+(2*1)=13

<em>(for these ones I divided it up into three parts; one were each star begins making it appear that there is a small rectangle on top of a medium rectangle on top of a large rectangle)</em>

and the bottom is 4*3=12

so then you add them all up

6+3+3+3+3+6+12+13+13+12

that all equals 74

I hope this helps!

5 0

3 years ago

Read 2 more answers

Mahni plans to spend the next 12 weeks saving some of her income. She will save $x a week for the first 6 weeks and then $(2x −

Ulleksa [173]

$x=213$

For first six weeks she saved 213$