Question 9 (10 points)

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

2 years ago

What is the y-coordinate of the point that divides the directed

e-lub [12.9K]

Answer:

(D)5

Step-by-step explanation:

Given the point J(-3,1) and K(8,11).

The line segment that divides the segment from J to K in any given ratio can be determined using the formula.

$P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n}\right)$

In the given case:

$(x_1,y_1)=(-3,1), (x_2,y_2)=(8,11)$ , m:n=2:3

Since we are to determine the y-coordinate of the point that divides JK into a ratio of 2:3, we have:

$\dfrac{my_2+ny_1}{m+n}=\dfrac{2*11+3*1}{3+2}\\\\=\dfrac{22+3}{5}\\\\=\dfrac{25}{5}\\\\=5$

The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.

The correct option is D.

3 0

2 years ago

using the coordinate plane shown below 1/3 point is plotted five units to the right of -4, for where should a four point be plan

Mrac [35]

we know that

the fourth point is plotted 5 units to the right of (-4,4)

so

the coordinate x of the fourth point is equal to

-4+5=1

the y-coordinate of the fourth point is the same y coordinate of (-4,4)

therefore

the coordinates of the fourth point is (1,4)

8 0

1 year ago

In the graph shown, which ordered pair does NOT represent a solution to the graph?

andreyandreev [35.5K]

A) (1, 7) Doesn't
B) (0, 4) Doesn't
C) (2, –2) Doesn't
D) (3, –5) DOES

All the steps are right at the exception of line 7 (and onwards)

line 6 : 6x = 42 (it's right). Now divide both sides by 6:

line 7 should be: 6x/6 = 42/6
line 8 should be: x = 7.

8 0

3 years ago

Read 2 more answers

The numbers of students in the 8 schools in a district are given below. (Note that these are already ordered from least to great

Luba_88 [7]

Answer:The mean increases but the median stays the same.

Step-by-step explanation:

201 + 233 + 237 +255 +269+277+306 mean is 257 and median is 255

225 +233 + 237 +255 +269+277+306 mean is 260 and median is 255

8 0

2 years ago