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vladimir1956 [14]
3 years ago
8

A statistics instructor designed an exam so that the grades would be roughly normally distributed with a mean of and a standard

deviation of 1015. In the space provided, draw a sketch of this distribution and label the mean and, using the standard deviation, two additional points on the horizontal axis. (2 pts)

Mathematics
1 answer:
WARRIOR [948]3 years ago
4 0

Answer:

a) Figure attached

b) P(X\geq 90)=P(\frac{X-\mu}{\sigma}\geq \frac{90-\mu}{\sigma})=P(Z \geq\frac{90-75}{10})=P(z>1.5)

And we can find this probability with the normal standard table and with the complement rule:

P(z\geq 1.5)=1-P(z

Step-by-step explanation:

A statistics instructor designed an exam so that the grades would be roughly normally distributed with a mean of μ=75 and a standard deviation of σ= 10.

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

Figure attached.

Part b

What proportion of students are expected to earn grades of ≥90?

We are interested on this probability

P(X\ geq 90)

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(X\geq 90)=P(\frac{X-\mu}{\sigma}\geq \frac{90-\mu}{\sigma})=P(Z \geq\frac{90-75}{10})=P(z>1.5)

And we can find this probability with the normal standard table and with the complement rule:

P(z\geq 1.5)=1-P(z

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2 years ago
What are the solutions?<br>8x^2-12x-23=-5​
erastova [34]

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Step-by-step explanation:

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Add 3/4 to both sides:

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3 years ago
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Step-by-step explanation:

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We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

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It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

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That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

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With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

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7 0
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valentinak56 [21]

Answer:

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Step-by-step explanation:

The equation of a line in slope- intercept form is

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8 0
3 years ago
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