1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Agata [3.3K]
2 years ago
12

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

ormal population with variance 02 = 6. will have a sample variance 52(a) greater than 9.1;(b) between 3.462 and 10.745.
Mathematics
1 answer:
konstantin123 [22]2 years ago
8 0

Answer:

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

b)P(13.848Step-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^2And we can find this probability like this:P(13.848And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"

You might be interested in
If a point is equidistant from the endpoint of segment, then it is
Mashutka [201]

Hi

.... then it is  located on the perpendicular bisector.

7 0
3 years ago
Jina made $154 for 11 hours of work. at the same rate, how much would she make for 17 hours of work?
Lynna [10]
14$ per hour
238$ for 17 hours
6 0
3 years ago
Which of the following represents the diameter of the circle below?
Svetach [21]

Answer:

xy represents the diameter

7 0
2 years ago
A bus makes 28 stops every 2 hours how many stops does it make in 3 hours
denis-greek [22]
28÷2=14
The bus makes 14 stops every hour
14×3=42
The bus makes 42 stops in 3 hours

Hope my answer helped u :)
6 0
3 years ago
Read 2 more answers
Given the two points (0,4) and (2, 6), what would the numerator of the equation for slope be?
serious [3.7K]
6-4 because the equation for slope is m=y2-y1/x2-x1
6 0
2 years ago
Read 2 more answers
Other questions:
  • What is the common ratio for the sequence 5, -10, 20, -40, ...?
    9·2 answers
  • Can someone pls tell me what I should press plss and thank you
    13·1 answer
  • wrote the fraction or mixed number as a money amount, and as a decimal in terms of dollars 65/100 and 1 48/100
    11·2 answers
  • 162 ⋅ 90 238·56 238 ⋅ 34 =
    10·2 answers
  • Which characteristics do the functions have in common? Select two options.
    10·1 answer
  • Suppose that the area of square lawn is 25x^2+40x+16
    8·1 answer
  • Select the quadratic expression that represents the product below.
    15·1 answer
  • Question 1(Multiple Choice Worth 1 points)
    5·1 answer
  • Un dirigible que está volando a 800 m de altura, distingue un pueblo con un ángulo de depresión de 12°. ¿A qué distancia del pue
    5·1 answer
  • Round your answer to the nearest hundredth.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!