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DedPeter [7]
2 years ago
5

If students’ scores were normally distributed and the mean was 200 with a standard deviation of 40, then what is the probability

, in percentages, that it is below 240?

Mathematics
1 answer:
Sonja [21]2 years ago
4 0

Answer:

  84%

Step-by-step explanation:

The empirical rule tells you that 68% of the standard normal distribution is within 1 standard deviation of the mean. The distribution is symmetrical, so the amount in the lower tail is (1 -68%)/2 = 16%.

Since the number you're interested in, 240, is one standard deviation above the mean (200 +40), the percentage of interest is the sum of the area of the central part of the distribution along with the lower tail:

  68% + 16% = 84%.

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3 years ago
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC =16 and DC=5 what is the length of BC in the simplest ra
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The length of BC is 4 \sqrt{5}.

Solution:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 16 and DC = 5

<u>Leg rule of geometric mean theorem:</u>

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

$\Rightarrow \frac{AC}{BC}=\frac{BC}{DC}$

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Do cross multiplication.

\Rightarrow  16\times 5 = x\times x

\Rightarrow  80= x^2

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Taking square root on both sides.

\Rightarrow  \sqrt{16\times 5} = \sqrt{x^2}

\Rightarrow  \sqrt{4^2\times 5} = \sqrt{x^2}

square and square roots get canceled, we get

\Rightarrow  4\sqrt{ 5} = x

The length of BC is 4 \sqrt{5}.

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Answer:

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Answer:

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Step-by-step explanation:


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