You have less than three hours to finish your homework which one of the following graphs represent the situation

In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a s

Oksi-84 [34.3K]

Answer:

a) $\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

b) From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

c) $P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

$P(Z\geq2.070)=1-P(Z$

Step-by-step explanation:

Let X the random variable the represent the scores for the test analyzed. We know that:

$\mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4$

And we select a sample size of 64.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Part a

For this case the mean and standard error for the sample mean would be given by:

$\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

Part b

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

Part c

For this case we want this probability:

$P(\bar X \geq 285)$

And we can use the z score defined as:

$z=\frac{\bar x -\mu}{\sigma_{\bar x}}$

And using this we got:

$P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

And using a calculator, excel or the normal standard table we have that:

$P(Z\geq2.070)=1-P(Z$

8 0

3 years ago

WORTH 10 points.

Tanya [424]

The answer is B because I did the math

8 0

3 years ago

Write an inequality that represents the verbal expression. All real numbers greater than or equal to 38.

Natasha_Volkova [10]

That inequality would be n ≥ 38

7 0

3 years ago

Rana's computer repair service charges $45/h. Bill's computer repair service charges a flat fee of $25 plus $18/h. Each company

Dmitry [639]

Answer

I not sure but what i would say is b. or if not c.

Step-by-step explanation:

8 0

3 years ago

What value of x makes the equation true? 3(4x-5)-4x+1=-6 Please show work

V125BC [204]

Answer:

x = 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3(4x - 5) - 4x + 1 = -6

Step 2: Solve for x

Distribute 3: 12x - 15 - 4x + 1 = -6
Combine like terms: 8x - 14 = -6
Isolate x term: 8x = 8
Isolate x: x = 1

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 3(4(1) - 5) - 4(1) + 1 = -6
Multiply: 3(4 - 5) - 4 + 1 = -6
Subtract: 3(-1) - 4 + 1 = -6
Multiply: -3 - 4 + 1 = -6
Subtract: -7 + 1 = -6
Add: -6 = -6

Here we see that -6 does indeed equal -6.

∴ x = 1 is the solution to the equation.

3 0

2 years ago