Find the area of the figure shown below and type your result in the empty box.<br><br><br>

Assume the sample variances to be continuous measurements. Find the probability that a random sample of 25observations, from a n

konstantin123 [22]

Answer:

a) $P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

b) $P(13.848$ Step-by-step explanation:

Previous concepts

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

For this case we assume that the sample variance is given by $S^2$ and we select a random sample of size n from a normal population with a population variance $\sigma^2$ . And we define the following statistic:

$T = \frac{(n-1) S^2}{\sigma^2}$

And the distribution for this statistic is $T \sim \chi^2_{n-1}$

For this case we know that n =25 and $\sigma^2 = 6$ so then our statistic would be given by:

$\chi^2 = \frac{(n-1)S^2}{\sigma^2}=\frac{24 S^2}{6}= 4S^2$

With 25-1 =24 degrees of freedom.

Solution to the problem

Part a

For this case we want this probability:

$P(S^2 > 9.1)$

And we can multiply the inequality by 4 on both sides and we got:

$P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

And we can use the following excel code to find it: "=1-CHISQ.DIST(36.4,24,TRUE)"

Part b

For this case we want this probability:

$P(3.462 < S^2$

If we multiply the inequality by 4 on all the terms we got:

$P(3.462*4 < 4S^2 < 4*10.745)= P(13.848< \chi^2$ And we can find this probability like this: $P(13.848$ And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"

8 0

3 years ago

Polygon with three interior angles whose sum 180 degrees

mojhsa [17]

Answer:

Triangle

Step-by-step explanation:

A triangle has three vertexes, and therefore three interior angles. Those angles also sum to 180 degrees because of the formula (n-2)*180, where n is the number of sides that a polygon has. Plugging in 3, you get $1\cdot 180$ , or just 180 degrees. Hope this helps!

6 0

3 years ago

Read 2 more answers

If 4 adult elephants eat 320 pounds of food, how many ounces of food should the zookeeper purchase?

fgiga [73]

Answer:

Step-by-step explanation:

5 0

3 years ago

What is Discount Comics is running a special: 20 comics for $5.00. Seth purchases 30 comics for $7.50. What is the sale price pe

Shalnov [3]

Since we are finding the unit rate of the cost per comic, we will need to divide $5 by 20 comics which you will get 0.25 cents and divide $7.50 by 30 comics which you will also get 0.25 cents.Therefore, the unit rate and constant of proportionality is 0.25 cents.

8 0

3 years ago

Read 2 more answers

Find point P that divides segments AB into a 2:3 ratio.

nasty-shy [4]

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
A(-3,1)\qquad B(3,5)\qquad
\qquad \stackrel{\textit{ratio from A to B}}{2:3}
\\\\\\
\cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-3,1)=2(3,5)\\\\
-------------------------------\\\\
P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)$

$\bf -------------------------------\\\\
P=\left(\cfrac{(3\cdot -3)+(2\cdot 3)}{2+3}\quad ,\quad \cfrac{(3\cdot 1)+(2\cdot 5)}{2+3}\right)
\\\\\\
P=\left(\cfrac{-9+6}{5}~~,~~\cfrac{3+10}{5} \right)\implies P=\left(-\frac{3}{5}~~,~~\frac{13}{5} \right)$

6 0

3 years ago

Find the area of the figure shown below and type your result in the empty box.​

Find the area of the figure shown below and type your result in the empty box.