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IgorC [24]
2 years ago
7

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

tudent guesses the whole test, the expected number of correct answers is 20 with a standard error of .Compute the z-test statistic for the observed value 13.Find the observed significance level or P-value of the statistic.
Mathematics
1 answer:
Cloud [144]2 years ago
5 0

Answer:

z=\frac{13-20}{4}=-1.75

Assuming:

H0: \mu \geq 20

H1: \mu

p_v = P(Z

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

X \sim Binom(n=100, p=0.2)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

We need to check the conditions in order to use the normal approximation.

np=100*0.2=20 \geq 10

n(1-p)=20*(1-0.2)=16 \geq 10

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

E(X)=np=100*0.2=20

\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4

So we can approximate the random variable X like this:

X\sim N(\mu =20, \sigma=4)

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".  The letter \phi(b) is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: \phi(b)=P(z

The z score is given by this formula:

z=\frac{x-\mu}{\sigma}

If we replace we got:

z=\frac{13-20}{4}=-1.75

Let's assume that we conduct the following test:

H0: \mu \geq 20

H1: \mu

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

p_v = P(Z

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Sliva [168]

the answer is 16

8^(4/3) can be written in different ways. You can first simplify it by breaking the exponents down into 1/3 and 4. You can write it as (8^1/3)^4 (it still means the same thing). When you raise something to the one over something fraction, the denominator tells you what the root is. Because it says 1/3, it means that you're finding the cube root of something. So you can rewrite it as (3√8)^4 (the three should be sitting on top of the sign to signify that it's cube root). You then just solve from there. The cube root of 8 is 2 (2*2*2=8) so it'll simplify to (2)^4. You then solve it from there and get 16 as your answer (2*2*2*2=16).

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3 years ago
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chubhunter [2.5K]
90000000000000000000000000000000000000000

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Use the distributive property two different ways to find the product of 127 and 32
cricket20 [7]
127 = 100 +27
32 = 30 +2
so 127 x 32 = (100 + 27) x (30+2) = (100x30) + (100x2) + (27x30) +(27x2)
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second way:

127 = 100 + 27
127 x 32 = (100+27) x 32 = (100x 32) + ( 27x32) = 3200 + 864 = 4064
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3 years ago
Please can you help me​
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A= 47
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Given r=3 and a center of (3,5)? Find the equation of the circle in standard and general form.
alukav5142 [94]

9514 1404 393

Answer:

  • (x -3)^2 +(y -5)^2 = 9
  • x^2 +y^2 -6x -10y +25 = 0

Step-by-step explanation:

The standard form equation for a circle of radius r and center (h, k) is ...

  (x -h)^2 +(y -k)^2 = r^2

For radius 3 and center (3, 5), this is ...

  (x -3)^2 +(y -5)^2 = 9 . . . . standard form equation

Expanding this and subtracting the constant on the right gives ...

  x^2 -6x +9 +y^2 -10y +25 -9 = 0

  x^2 +y^2 -6x -10y +25 = 0 . . . . general form equation

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2 years ago
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