Order from Greastest to least. Make sure you place the symbol between the numbers not a comma. 38,756 , 38, 475, 38, 657

A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 119. Co

hammer [34]

Answer:

a) $P(411$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1$

And the percentage would be 68.3%

b) For this case we can find this with the complement rule and with the result of the part a and we got:

$P(X649) = 1-P(411< X< 649) = 1-0.683 = 0.317$

And that represent 31.7%

c) $P(X>768)=P(\frac{X-\mu}{\sigma}>\frac{768-\mu}{\sigma})=P(Z>\frac{768-530}{119})=P(z>2)$

And we can find this probability with the complment rule like this:

$P(z>2)=1-P(z$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>2)=1-P(z$

And the percentage would be 2.3%

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".

Part a

Let X the random variable that represent the standardized test's

Where $\mu=530$ and $\sigma=119$

We are interested on this probability

$P(411$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(411$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1$

And the percentage would be 68.3%

Part b

For this case we can find this with the complement rule and with the result of the part a and we got:

$P(X649) = 1-P(411< X< 649) = 1-0.683 = 0.317$

And that represent 31.7%

Part c

$P(X>768)$

Using the z score we got:

$P(X>768)=P(\frac{X-\mu}{\sigma}>\frac{768-\mu}{\sigma})=P(Z>\frac{768-530}{119})=P(z>2)$

And we can find this probability with the complment rule like this:

$P(z>2)=1-P(z$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>2)=1-P(z$

And the percentage would be 2.3%

5 0

3 years ago

Question 4 of 12

posledela

Answer:

y - 22 = 14(x - 1)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 14x - 3 ← is in slope- intercept form

with slope m = 14

Parallel lines have equal slopes

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 14 and (a, b) = (1, 22) , then

y - 22 = 14(x - 1)

8 0

3 years ago

Cory knows that 16 tablespoons are the same as 1 cup. He measures3/4 cup, but all he has is a tablespoon. How many table spoons

nadya68 [22]

he should use 12 tablespoons

8 0

3 years ago

Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation

AleksAgata [21]

Answers:

- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t>
- parametric equations:
x = 1 + 6t
y = -1 + 7t
z = 7 - 6t

Explanation:

To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,

v = q - p
= (7,6,1) - (1,-1,7)
v = (6, 7, -6)

The vector equation of the line is given by

$r(t) = v_0 + tv$

Where

$v_0$ = a point in the line (we choose point p(1,-1,7))

So, the equation of the line joining p and q is given by

$r(t) = v_0 + tv
\\ \indent = \left \langle 1, -1, 7 \right \rangle + t\left \langle 6, 7, -6 \right \rangle
\\ \indent = \left \langle 1, -1, 7 \right \rangle + \left \langle 6t, 7t, -6t \right \rangle
\\ \indent \boxed{r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle }$

In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.

Since the vector equation is given by

$r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle$

The parametric equations of the line are given by:

$x(t) = 1 + 6t
\\y(t) = 1 + 7t
\\z(t) = 7 - 6t$

4 0

3 years ago

A city worker is painting a stripe down the center of Main Street. Main Street is 8/10 mile long. the worker painted 4/10 mile o

Lilit [14]

8/10-the length of the street minus 4/10-the completed amount equals 4/10 of a mile is the remaining. Since the denominators are the just sub the numerator.

4 0

3 years ago