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4 years ago

The medians of a triangle intersect at a point called the

Mathematics

1 answer:

lapo4ka [179]4 years ago

8 0

Answer:

The medians of a triangle intersect at a point called the

centroid of the triangle

Step-by-step explanation:

The median of a triangle is a segment joining any vertex to the midpoint of the opposite side. The medians of a triangle are concurrent (they intersect in one common point). The point of concurrency of the medians is called the centroid of the triangle.

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat

zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5$

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

$Z = \frac{205 - 200}{5}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 195

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

$Z = \frac{195 - 200}{5}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

$Z = \frac{210 - 200}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

X = 195

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

$Z = \frac{190 - 200}{5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0

3 years ago

Mitchell went on a shopping trip to Kensington. He purchased a pair of headphones originally priced at $50 but discounted 60%. I

MrRa [10]

Answer:

$24.50

Step-by-step explanation:

60% of $50= $30

$50-$30= $20

15% of $20= $4.50

$20+$4.50= $24.50

8 0

3 years ago

Read 2 more answers

Hey guys please help!!

Advocard [28]

Answer:

Yes

Step-by-step explanation:

g(x) = - $\frac{1}{4}$ x + $\frac{1}{4}$

y = - $\frac{1}{4}$ x + $\frac{1}{4}$ ....... (1)

(1) × 4

4y = - x + 1

x = - 4y + 1

y = - 4x + 1

f(x) = - 4x + 1

∴ f(x) and g(x) are inverses

8 0

3 years ago

Write the equation of the line that is per to x = -3 and passes through the point (4,-7)

Anon25 [30]

Answer:

y=-1/3x-17/3

Step-by-step explanation:

I assume you mean perpendicular to x=-3.

In that case, we would flip and take the negative. A perpendicular slope would be x=-1/3

Now we plug the point (4,-7) into the equation

y=mx+b

y=-1/3x+b

-7=-1/3*4+b

-7=-4/3+b

b= -17/3

The whole equation would be:

y=-1/3x-17/3

I hope this helps! :)

8 0

3 years ago

Jim has received scores of 72 72 and 77 77 on his first two 100 point tests. what score must he get on his third 100 point test

Alisiya [41]

77+72=149
149/2=74.5
through the process of elimination, I found that Jim needs to get an 88 or higher to receive an average of 79 or greater.

77+72+88=237
237/3=79

7 0

3 years ago