Some students paid a private tutor to them improve their results on a certain mathematical test. these students had a mean change in score of plus17 points, with a standard deviation of 67 points. in a random sample of 100 students who pay a private tutor to them improve their results, what is the likelihood that the change in the sample mean score is less than 10 points?

Tt is unlikely to have change in the sample mean score is less than 10 points .

Step-by-step explanation:

Given : Mean :

Standard deviation :

Sample size : n= 100

We assume that the change in students scores are normally distributed.

Let X be the random variable that represents the change in students scores .

Z score :

For x = 10

By using the standard normal distribution table , the probability  that the change in the sample mean score is less than 10 points :-

Since the calculated probability is less than 0.5.

So , we say that it is unlikely to have change in the sample mean score is less than 10 points .

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3