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 a sample of 16 students’ IQ scores from a statistics class at UT. What is the shape of this sampling distribution?

Where and

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

Because by definition:

And for this case we have this:

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:

Where and

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

Because by definition:

And for this case we have this:

sum= when you add is how much the whole amount is

distance= when you use angles and it means how far it goes

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3