What is the area of this shape

It is known that IQ scores form a normal distribution with a mean of 100 and a standard deviation of 15. If a researcher obtains

sdas [7]

Answer:

$X \sim N(100,15)$

Where $\mu=100$ and $\sigma=15$

We select a sample of n=16 and we are interested on the distribution of $\bar X$ , since the distribution for X is normal then we can conclude that the distribution for $\bar X$ is also normal and given by:

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

Because by definition:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$E(\bar X) = \mu$

$Var(\bar X) = \frac{\sigma^2}{n}$

And for this case we have this:

$\mu_{\bar X}= \mu = 100$

$\sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75$

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

$X \sim N(100,15)$

Where $\mu=100$ and $\sigma=15$

We select a sample of n=16 and we are interested on the distribution of $\bar X$ , since the distribution for X is normal then we can conclude that the distribution for $\bar X$ is also normal and given by:

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

Because by definition:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$E(\bar X) = \mu$

$Var(\bar X) = \frac{\sigma^2}{n}$

And for this case we have this:

$\mu_{\bar X}= \mu = 100$

$\sigma_{\bar X} = \frac{15}{\sqrt{16}}= 3.75$

6 0

3 years ago

Find the sum of the integers from -6 to 57<br> A. 1,500<br> B. 1,621<br> C. 1,734<br> D. 1,512

krek1111 [17]

Answer: it D. 1,512

Step-by-step explanation: i hop this helps if it wrong sorry about that

4 0

3 years ago

Find cos x if sin x =0.82.

True [87]

Answer:

cosx= 35. Use Trignometrical identity cosx = √1−sin2x . cos x = √1−1625 = √925 = 35 to be the ...

Missing: =0.82 ‎| Must include: =0.82

Step-by-step explanation:

5 0

3 years ago

The height of a right cylinder is 3 times the radius of e base. The volume of the cylinder is 24π cubic units. What is the heigh

Nimfa-mama [501]

Volume = pi * r^2 * h
h = 3r
pi * r^2 * (3r) = 24 pi
3r^3 = 24
r^3 = 8
r = 2

Height = 3*2 = 6 units

6 0

3 years ago

Read 2 more answers

3x/4-7/2=1/4 what does x equal

LUCKY_DIMON [66]

Answer:

x=5

Step-by-step explanation:

I did math and ForGOt

7 0

3 years ago