MATHEMATICS COLLEGE

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 student 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.

Answers

Answer 1

Answer:

Answer:

$z=(13-20)/(4)=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu <20$

$p_v = P(Z<-1.75) = 0.0401$

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:

$nCx=(n!)/((n-x)! x!)$

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:

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

$\sigma=√(np(1-p))=√(100*0.2(1-0.2))=4$

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: $\phi(b)=P(z<b)$

The z score is given by this formula:

$z=(x-\mu)/(\sigma)$

If we replace we got:

$z=(13-20)/(4)=-1.75$

Let's assume that we conduct the following test:

H0: $\mu \geq 20$

H1: $\mu <20$

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:

$p_v = P(Z<-1.75) = 0.0401$

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An office will increase salary to its top 8% employees on the basis of a performance score the office created for each employee. The performance score is approximately normal with mean 82.5 and standard deviation 9.25. How high must an employee score in order to qualify for increase in the salary?

Answers

Answer:

An employee's score in order to qualify for increase in the salary must be higher than 95.45.

Step-by-step explanation:

Let X represent the performance score of employees.

It is provided that X follows a normal distribution with parameters μ = 82.5 and σ - 9.25.

It is provided that the office will increase salary of its top 8% employees on the basis of a performance score the office created for each employee.

That is, the probability to qualify for increase in the salary is,

P (X > x) = 0.08

⇒ P (X < x) = 0.92

⇒ P (Z < z) = 0.92

The corresponding z-value is,

z = 1.40

Compute the value of x as follows:

$z=(x-\mu)/(\sigma)\n\n1.40=(x-82.5)/(9.25)\n\nx=82.5+(1.40* 9.25)\n\nx=95.45$

Thus, an employee's score in order to qualify for increase in the salary must be higher than 95.45.

Please help I'm really bad at math and I can't get a bad grade can someone help me please max points

Answers

1.closed circle means equal to

line to the right means greater than

x>= 4

2. open circle means not equal to

line to the left and right means not equal to

x not equal to -4

Choice C

3. less than means open circle and line to the left

x<-3

Choice A

4. m<=-1

closed circle because of the equals

line to the left

Choice B

5. y <6

open circle because of no equals

line to the left

Choice B

6. t>=0

closed circle with the =

line to the right

Choice A

7. x not equal to -4

open circle at 4

lines going both directions

Choice B

8.n <=-1.5

closed circle at -1.5

line going to the left

Choice C

1. x greater than or equal to 4 (B)

2. x does not equal 4 (C)

3. A

4. B

5. B

6. A

7. B

8. C

(The pictures were out of order but i did it by number shown in the pictures. Hope this helps.)

Derive cos (2x - 1)

Answers

Answer:

Step-by-step explanation:

I believe that what you want to do here is to "differentiate" cos (2x - 1).

We must use the rule for differentiating cos x and also the chain rule, since the input to cos x here is (2x - 1).

(d/dx) is the derivative operator.

(d/dx) (cos x) = -sin x

(d/dx) cos (2x - 1) = - sin (2x - 1) * (d/dx) (2x -1) = -sin (2x - 1)(2) = -2sin (2x - 1)

6^3x=14 Show your work

Answers

Answer:

Is 3x supposed to be an exponent?

Step-by-step explanation:

Both possible answer are provided

3x as an exponent and as 6 times 3x

Please help me thank you

Answers

Answer:

Step-by-step explanation:

b = a^2/4 +4

Let a =8

b = 8^2 /4 +4

= 64/4 +4

= 16 +4

= 20

Answer:

b = 20 when a = 8.

Step-by-step explanation:

For this problem, we will simply plug the value of a=8 into the given equation for b, to find the value of b.

b = [ (a)^2 / 4 ] + 4

b = [ (8)^2 / 4 ] + 4

b = [ 64 / 4 ] + 4

b = [ 16 ] + 4

b = 20

Hence, when the value of a=8, then the value of b=20.

Cheers.

Explain how 7/10 and 70/100 are equivalent decimals

Answers

It is proved that the given decimals are equivalent decimals.

What are equivalent fractions? What is a mathematical function, equation and expression?

equivalent fractions : Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.