The geometric average of -12%, 20%, and 25% is ________

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

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 0.95 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: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

5 0

2 years ago

What is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6

Mashutka [201]

The answer is C. The numerator 7x+14 can be factored as 7(x+2). The denominator 2x^2+2x-6 can be factored as (x+2)(2x-3). The greatest common divisor of 7(x+2) and (x+2)(2x-3) is obviously x+2, which is contained in both of the two expressions.

4 0

2 years ago

If a lot contains 48,000 square feet and is 240' wide, how deep is the lot?

lisabon 2012 [21]

We would assume the lot takes a rectangular shape. With that in mind. the area of the rectangular plot is 48, 000 and its width is 240. We only need to know the area of a rectangle which is L * W.
So 48, 000 = L * 240
L = 48, 000/ 240
L = 200
It is 200 square feet deep.

6 0

2 years ago

You invested a total of $12,000 at 4.5 percent and 5 percent simple interest. During one year, the two accounts earned $570. How

Luda [366]

Answer: You invested $6000 in both accounts.

Step-by-step explanation:

Let x represent the amount invested in the account earning 4.5% interest.

Let y represent the amount invested in the account earning 5% interest.

You invested a total of $12,000 at 4.5 percent and 5 percent simple interest. This means that

x + y = 12000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

Considering the account earning 4.5%

I = (x × 4.5 × 1)/100 = 0.045x

Considering the account earning 5%

I = (y × 5 × 1)/100 = 0.05y

During one year, the two accounts earned $570. . This means that

0.045x + 0.05y = 570 - - - - - - - - - - 1

Substituting x = 12000 - y into equation 1, it becomes

0.045(12000 - y) + 0.05y = 570

540 - 0.045y + 0.05y = 570

- 0.045y + 0.05y = 570 - 540

0.005y = 30

y = 30/0.005 = 6000

x = 12000 - y = 12000 - 6000

x = $6000

6 0

2 years ago

The floor area of a hall is 1044 m2. The length is 36 m. Give a quick estimate of width of the hall. ?

wolverine [178]

36m. Im not sure but thats what i got, hope it helps...

4 0

2 years ago

The geometric average of -12%, 20%, and 25% is _________.