Which ordered pair must be a solution in the graph of the leaner inequality below?

The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This

Katarina [22]

Answer:

a) $\hat \mu = \bar X = 145$

b) $145-1.64\frac{35}{\sqrt{25}}=133.52$

$145+1.64\frac{35}{\sqrt{25}}=156.48$

So on this case the 90% confidence interval would be given by (133.52;156.48)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X=145$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=35$ represent the population standard deviation

n=25 represent the sample size

a) For this case the best point of estimate for the population mean is the sample mean:

$\hat \mu = \bar X = 145$

b) Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$145-1.64\frac{35}{\sqrt{25}}=133.52$

$145+1.64\frac{35}{\sqrt{25}}=156.48$

So on this case the 90% confidence interval would be given by (133.52;156.48)

3 0

3 years ago

Solve using Elimination and find the value of x. 4x + 8y = 20-4x + 2y = -30

olchik [2.2K]

x= 17/2 (as a fraction)

y= -8

(x,y)= (17/2, -8)

6 0

4 years ago

A word problem for 460 - 65x < 100

gtnhenbr [62]

<h3>Answer</h3>

$\sf \large \:　 \green{↬}460 - 65x < 100$

$\: \: \:$

Subtract 460 from both sides:

$\sf \large \:　 \green{↬}460 - 65x - 460 < 100 - 460$

$\: \:$

$\sf \large \:　 \green{↬} - 6x + 460 - 460 < 100 - 460$

$\: \:$

$\sf \large \:　 \green{↬} - 65x < 100 - 460$

$\: \: \:$

$\sf \large \:　 \green{↬}65x < - 360$

$\: \: \:$

Hope Helps! :)

3 0

3 years ago

What is the equation of the line which includes points HELP ASAP

Harman [31]

Answer:

OPTION C

OPTION A

OPTION C

Step-by-step explanation:

We use two - point form to determine the equation of the line when two points are given.

The two - point form is: $\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the two points passing through it.