The measures of the angles of a triangle are shown in the figure below. Solve

Explanation A random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a stan

Olenka [21]

Answer:

The 95% confidence interval would be given by (81.933;84.467)

Step-by-step explanation:

1) 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".

$\bar X=83.2$ represent the sample mean

$\mu$ population mean (variable of interest)

s=6.4 represent the sample standard deviation

n=100 represent the sample size

Confidence interval

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:

$df=n-1=100-1=99$

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(0.025,99)".And we see that $t_{\alpha/2}=1.98$

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

$83.2-1.98\frac{6.4}{\sqrt{100}}=81.933$

$83.2+1.98\frac{6.4}{\sqrt{100}}=84.467$

So on this case the 95% confidence interval would be given by (81.933;84.467)

7 0

3 years ago

I NEED HELP PLEASE 10 POINTS

densk [106]

Answer:

Yes, it is proportional because it has a constant rate of change. I think so at least.

Step-by-step explanation:

Every day she loses $5.

6 0

3 years ago

the greatest volcanic eruption in recorded history took place in 1815 on the indonesian island of sumbawa, when the volcano tamb

algol [13]

Answer:

$166\frac{2}{3}\ m$

Step-by-step explanation:

Let

x ----> the average depth of the resulting layers of ash and rock

we know that

To find out the average depth, divide the cubic kilometers of molten rock by the area where all the ejected material fell.

so

$\frac{100\ km^3}{600\ km^2}=\frac{1}{6}\ km$

Convert to meters

Remember that

$1\ km=1,000\ m$

so

$\frac{1}{6}\ km=\frac{1}{6}(1,000)=\frac{1,000}{6}=\frac{500}{3}\ m$

Convert to mixed number

$\frac{500}{3}\ m=\frac{498}{3}+\frac{2}{3}=166\frac{2}{3}\ m$

7 0

3 years ago

Confused! Please help and show how you did it.

natta225 [31]

The formula for the area is length times width, so for question 17, multiply those two numbers together.

If he drives 9 miles to work per day and works 5 days a week, you would need to get the total of miles per week. Then, once you do, multiply that number by 52.

7 0

3 years ago

1/2 or (1/2)² which value is greater

Ket [755]

Answer:

when a expression is squared (²) that means it is multiplyed by itself.

Step-by-step explanation:

(1/2)² = (1/2 x 1/2)

1 squared = 1

2 squared = 4

1/4 is smaller than 1/2. 1/2 is greater than (1/2)²

3 0

3 years ago