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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

Mt. Pleasant elemantry School was collecting canned food. The chart below shows how much food they collected over 3 weeks the ca

n200080 [17]

Just -: by 8 I think

4 0

3 years ago

The data in which table represents a linear function that has a slope of zero? A 2-column table with 5 rows. Column 1 is labeled

lisov135 [29]

Answer: A 2-column table with 5 rows. Column 1 is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1. Column 2 is labeled y with entries 5, 5, 5, 5, 5.

8 0

3 years ago

OMG PLEASE Help me !!!! ILL GIVE YOU BRAINLIEST !!! Explain in order to get it

Doss [256]

Answer:

I'm not sure but I believe the correct answer is line L2.

Step-by-step explanation:

It seems to be closer to more points than the other lines.

If it is not L2, it must be L3.

4 0

3 years ago

Suppose you are taking the bus home, and can take either Route 51 or Route 82. You know that the Route 82 will arrive at the bus

kykrilka [37]

Answer:

E[T] = 10

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the expected value of the uniform distribution is given by:

$E = \frac{a+b}{2}$

Uniformly distributed between 0 and 20 minutes.

This means that $a = 0, b = 20$

Let T be the number of minutes you wait until you board a bus. Find E[T].

This is

$E[T] = \frac{a + b}{2} = \frac{0 + 20}{2} = 10$

E[T] = 10

8 0

3 years ago

Wht are y'all doing​

Wht are y'all doing