Convert equation from slope intercept form to standard form y=-7/3x+1

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$

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

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

7 0

3 years ago

On a map, 9 cm represents 15 miles. If the distance between two cities on the map is 15 cm, how many miles separate the cities?

torisob [31]

Answer:

15 cm on the map is equal to 25 miles.

Step-by-step explanation:

Given that,

On a map, 9 cm represents 15 miles.

The distance between two cities is 15 cm. We need to find the distance in miles.

9 cm = 15 miles

$1\ cm=\dfrac{15}{9}\ \miles$

So, 15 cm is equal to,

$15\ cm=\dfrac{15}{9}\times 15\ miles\\\\=25\ miles$

So, 15 cm on the map is equal to 25 miles.

4 0

3 years ago

If two lines are perpendicular describe the relationship between their slopes

Aloiza [94]

Perpendicular lines have slopes that are negative reciprocals. example: line a has a slope of 2/3, line b has a slope if -3/2 if they are perpendicular.

7 0

3 years ago

Find the value of m. 4(m-2) = 24

slega [8]

4(m-2)=24

4m-8=24 distributive property

add 8 to each side

4m=32

divide each side by 4

m=8

4 0

2 years ago

Read 2 more answers

Help me please im not good a this

Ghella [55]

0,-5 i hope this is can sorry if its wrong

3 0

3 years ago

Convert equation from slope intercept form to standard form￼ y=-7/3x+1

Convert equation from slope intercept form to standard form y=-7/3x+1