Which number sentence is an example of the identity property of addition?

nordsb [41]

I was stuck on the same thing in my class test. I ended up failing but if I get the answers to it I’ll totally send them to you

7 0

3 years ago

4. A random variable X has a mean of 10 and a standard deviation of 3. If 2 is added to each value of X, what will the new mean

Ede4ka [16]

Adding 2 to each value of the random variable $X$ makes a new random variable $X+2$ . Its mean would be

$E[X+2]=E[X]+E[2]=E[X]+2$

since expectation is linear, and the expected value of a constant is that constant. $E[X]$ is the mean of $X$ , so the new mean would be

$E[X+2]=10+2=12$

The variance of a random variable $X$ is

$V[X]=E[X^2]-E[X]^2$

so the variance of $X+2$ would be

$V[X+2]=E[(X+2)^2]-E[X+2]^2$

We already know $E[X+2]=12$ , so simplifying above, we get

$V[X+2]=E[X^2+4X+4]-12^2$

$V[X+2]=E[X^2]+4E[X]+4-12^2$

$V[X+2]=(V[X]+E[X]^2)+4E[X]-140$

Standard deviation is the square root of variance, so $V[X]=3^2=9$ .

$\implies V[X+2]=(9+10^2)+4(10)-140=9$

so the standard deviation remains unchanged at 3.

NB: More generally, the variance of $aX+b$ for $a,b\in\mathbb R$ is

$V[aX+b]=a^2V[X]+b^2V[1]$

but the variance of a constant is 0. In this case, $a=1$ , so we're left with $V[X+2]=V[X]$ , as expected.

5 0

3 years ago

Suppose a brand of light bulbs is normally distributed, with a mean life of 1300 hr and a standard deviation of 50 hr. Find the

tatyana61 [14]

Answer:

Step-by-step explanation:

Since the life of the brand of light bulbs is normally distributed, we would apply the the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = life of the brand of lightbulbs

u = mean life

s = standard deviation

From the information given,

u = 1300 hrs

s = 50 hrs

We want to find the probability that a light bulb of that brand lasts between 1225 hr and 1365 hr. It is expressed as

P(1225 ≤ x ≤ 1365)

For x = 1225,

z = (1225 - 1300)/50 = - 1.5

Looking at the normal distribution table, the probability corresponding to the z score is

0.06681

For x = 1365,

z = (1365 - 1300)/50 = 1.3

Looking at the normal distribution table, the probability corresponding to the z score is

0.9032

Therefore

P(1225 ≤ x ≤ 1365) = 0.9032 - 0.06681 = 0.8364

7 0

3 years ago

Find the distance between the points (13,5) and (10,1)

ElenaW [278]

The distance is (3,4)

Simply subtract the x and y functions.

13 - 10 = 3

5 - 1 = 4

8 0

3 years ago

I need help with this question can someone please help me?

zlopas [31]

Answer: y= -1/1x - 1

Okay, to find the equation you must find the y-intercept and the slope.

To find the y-intercept, you must find (0,y). This is the point on the y-axis where x is 0. So, where along the y-axis is there a point? There is a point at (0,-1). Therefore, your y-intercept is -1.

To find the slope, you must do rise/run. Go to a point on the line, such as (0,-1). You must go up (or down) until you get lined up with next point on the line. You go up one time. Then, you must go right (or left) to get to the exact point. In this case, the point would be (-1,0). You go left one time.

If you go down or left when doing rise/run, the number would be negative. Since you went left, that number would be negative.

So, our slope would be 1/-1, which can also be written as -1/1.

Now, write the equation. There is always an x next to the slope. y= -1/1x

Then, put the y-intercept next to it. If it is positive, use a +. If it is negative, use a -. It is negative.

Therefore, the answer is y= -1/1x -1.

5 0

3 years ago