Solve the inequality<br> x/3

SAT scores (out of 2400) are distributed normally with a mean of 1500 and a standard deviation of 300. Suppose a school council

alekssr [168]

Answer:

10.78% probability this student's score will be at least 2200

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Conditional probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

$\mu = 1500, \sigma = 300$

We pick a recognized student. What is the probability this student's score will be at least 2200

Event A: Recognized(scored at least 1900).

Event B: At least 1900.

Probability of scoring at least 1900.

1 subtracted by the pvalue of Z when X = 1900. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1900 - 1500}{300}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082.

1 - 0.9082 = 0.0918.

So P(A) = 0.0918

Intersection:

The intersection between at least 1900 and at least 2200 is at least 2200.

Probability:

1 subtracted by the pvalue of Z when X = 2200. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2200 - 1500}{300}$

$Z = 2.33$

$Z = 2.33$ has a pvalue of 0.9901.

So $P(A \cap B) = 1 - 0.9901 = 0.0099$

Then

$P(B|A) = \frac{0.0099}{0.0918} = 0.1078$

10.78% probability this student's score will be at least 2200

4 0

3 years ago

10 cm

attashe74 [19]

Answer:

80

Step-by-step explanation:

Because you do 10*8=80

4 0

3 years ago

Vika [28.1K]

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-----------------------------\\\\
\cfrac{s^3}{s^3}\implies \cfrac{216}{1000}\implies \cfrac{\sqrt[3]{216}}{\sqrt[3]{1000}}\implies \cfrac{s}{s}\impliedby \textit{similarity ratio}$

and simplify it away

3 0

4 years ago

What two numbers multiply to get -42 and add to 11

nataly862011 [7]

To find out the answer, let's factor out -42 (as if it's a positive number).

42: 1 x 42, 2 x 21, 3 x 14, 6 x 7.

With these given factors and due to the product being negative, we will go on and off with them being negative to find which sum up to 11.

Let's try 1 and 42.

-1 + 42 = 41
-42 + 1 = -41.

1 x 41 is not our answer.

Let's try 2 and 21.

2 - 21 = -19
-2 + 21 = 19

2 x 21 is not our answer.

Let's try 3 and 14.

-3 + 14 = 11
3 - 14 = -11.

Your answer is:

-3 and 14 sum up to 11 and make a product of -42.

-3 and 14 are your numbers.

I hope this helps!

8 0

3 years ago

Write the equation of the line with slope of 2 and y-intercept (0, 15).

mr_godi [17]

Answer:

y = 2x + 15

Step-by-step explanation:

The slope-intercept form of the equation of a line is

y = mx + b

where m is the slope, and b is the y-coordinate of the y-intercept.

slope = m = 2

y-intercept = b = 15

y = 2x + 15

3 0

3 years ago

Solve the inequality x/3 - 2 <4