Reduce into lowest terms

An accounting firm is planning for the next tax preparation season. From last years returns, the firm collects a systematic rand

Elena L [17]

Answer:

a)From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error for the mean would be:

$\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14$

b) We want this probability:

$P(\bar X >120)$

And we can use the z score formula given by:

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

And replacing we got:

$z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143$

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

$P( z>2.143) = 1-P(Z$

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error for the mean would be:

$\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14$

Part b

We want this probability:

$P(\bar X >120)$

And we can use the z score formula given by:

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

And replacing we got:

$z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143$

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

$P( z>2.143) = 1-P(Z$

4 0

3 years ago

sana is senior to Mona by 18 years after 6 years.Sana will be twice as old as Mona. find Mona,s percentage

Gwar [14]

Let
Present age of Sana = s
Present age of Mona = m

Sana is senior to Mona by 18 years
s=m+18............(1)

After 6 years
Sana will be = s+6
Mona will be = m+6
Then
Sana will be twice as old as Mona
(s+6)=2(m+6)
s+6=2m+12
s=2m+12-6
s=2m+6.............(2)
Put the value of s from (2) to (1)
2m+6=m+18
2m-m=18-6
m=12
Put the value of m in (1)
s=m+18
s=12+18
s=30

Present age of Sana = s = 30 years old
Present age of Mona = m = 12 years old

3 0

3 years ago

PIT_PIT [208]

Let's start with a picture.

We see RST is smaller, and BC is parallel to but in the opposite direction to its corresponding segment ST. Both have slope -1.

If we look at the difference of points (technically called vectors but we don't have to go there) we get

C-B=(-2,2)

T-S=(1,-1)

Without further calculation we can see T-S is half the length of C-B.

The problem asks for a dilation followed by a reflection. We know the dilation scale is k=1/2 because the new triangle is half the size.

After dilation we get A'B'C':

A'(3,2), B'(-1,0), C'(-2,1)

We see now we need a reflection that flips the coordinates x and y. That's the +45° line through the origin, namely y=x.

Answer: k=1/2, y=x

7 0

3 years ago

Read 2 more answers

If f(x) = 2x^2 + 1 and g(x) = x^2 - 7, find (f+g)(x)

jarptica [38.1K]

(f + g)(x) means f(x) + g(x)

So, you just input the function of f(x) and g(x) altogether, then simplify it.
(f + g)(x)
= f(x) + g(x)
= 2x² + 1 + x² - 7
= 2x² + x² + 1 - 7
= 3x² - 6

The answer is b

5 0

3 years ago

I will give brainliest if anyone answers this : Would you like to be my friend on brainly? :)

Artyom0805 [142]

Answer:

alr then bet

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers