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3 years ago

SOMEONE PLZ HELP IM SO LOST ILL GIVE U BRAINLIEST

Mathematics

1 answer:

hammer [34]3 years ago

6 0

Answer:

What is a Proof?

A series of steps, with justifications, that verifies a theorem or relationship exists

Types of Proofs

Two-column Proofs a table with two columns; the first column is the mathematical statement, and the second column is the justification

Paragraph Proofs a type of proof that explains the rationale for each step using complete sentences in paragraph form

Flow Chart Proofs a diagram that contains the steps of the proof and the justification for each one

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Raw scores on a certain standardized test one year were normally distributed, with a mean of 156 and a standard deviation of 23.

s344n2d4d5 [400]

Answer:

About 220 of the students scored less than 96

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 156 and a standard deviation of 23.

This means that $\mu = 156, \sigma = 23$

Proportion that scored less than 96:

p-value of Z when X = 96. So

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

$Z = \frac{96 - 156}{23}$

$Z = -2.61$

$Z = -2.61$ has a p-value of 0.00453.

About how many of the students scored less than 96?

0.00453 out of 48592.

0.00453*48592 = 220.1.

Rounding to the closest integer:

About 220 of the students scored less than 96

3 0

3 years ago

Write an equation of the line passing through the given point and satisfying the given condition. Give the equation (a) in slope

Mariana [72]

Answer:

(a) y=8x-46

(b) 8x-y=46

Step-by-step explanation:

-y=-8x+4

y=8x+4

We know that 8 is the slope, and if we need a equation parallel to this line, then it will have the same slope.

Substitute (6,2)

2=8(6)+b

2=48+b

b=-46

The final answer is y=8x-46

7 0

3 years ago

Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 o

stepan [7]

Answer:

27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.

Step-by-step explanation:

To solve this problem, it is important to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$