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
PtichkaEL [24]
3 years ago
8

A particular brand of dishwasher soap is sold in three sizes: 35 oz, 45 oz, and 65 oz. Twenty percent of all purchasers select a

35-oz box, 50% select a 45-oz box, and the remaining 30% choose a 65-oz box. Let x1 and x2 denote the package sizes select by two independently selected purchasers. Determine the sampling distribution of X. Calculate E(X). Determine the sampling distribution of the sample variance S2. Calculate E(S2).
Mathematics
1 answer:
uysha [10]3 years ago
8 0

Answer:

E(X) = 44.5

E(S2) =  б^2 = 212.25

Step-by-step explanation:

Given:

- The possible value of x are: 25,40,65 with probabilities 0.2,0.5,0.3, respectively

Solution:

- There could be nine possible cases for the joint probability distribution.

                          [  x_1 ; x_2 ; p ( x_1 , x_2 ) = p ( x_1 )*p ( x_2 ) ]

        x_bar = (x_1 + x_2)/2  ,   s^2 = ( x_1 - x_bar )^2 + ( x_2 - x_bar )^2

- Now for all 9 possible cases we have:

 x_1 = 25 ; x = 25 ; p ( x_1 , x_2 ) = 0.04 ;  x_bar = 25 ; s^2 = 0

 x_1 = 25 ; x = 40 ; p ( x_1 , x_2 ) = 0.1 ;  x_bar = 32.5 ; s^2 = 112.5

 x_1 = 25 ; x = 65 ; p ( x_1 , x_2 ) = 0.06 ;  x_bar = 45 ; s^2 = 800

 x_1 = 40 ; x = 25 ; p ( x_1 , x_2 ) = 0.1 ;  x_bar = 32.5 ; s^2 = 112.5

 x_1 = 40 ; x = 40 ; p ( x_1 , x_2 ) = 0.25 ;  x_bar = 40 ; s^2 = 0

 x_1 = 40 ; x = 65 ; p ( x_1 , x_2 ) = 0.15 ;  x_bar = 52.5 ; s^2 = 312.5

 x_1 = 65 ; x = 25 ; p ( x_1 , x_2 ) = 0.06 ;  x_bar = 45 ; s^2 = 800

 x_1 = 65 ; x = 40 ; p ( x_1 , x_2 ) = 0.15 ;  x_bar = 52.5 ; s^2 = 312.5

 x_1 = 65 ; x = 65 ; p ( x_1 , x_2 ) = 0.09 ;  x_bar = 65 ; s^2 = 0

- The probability distribution of  x_bar:

 x_bar  =       25          32.5         40          45           52.5            65

 P ( x )  =       0.04       0.20       0.25        0.12         0.30           0.09    

- Expected value of x_bar:

E ( x_bar) = sum ( x_bar*p ( x ) )

                 = 25*(0.04)+32.5*(0.02)+40*(0.25)+45*(0.12)+52.5*(0.3)+65*(0.09)

                 = 1 + 6.5 + 10 + 5.4 + 15.75 + 5.85

                 = 44.5

- The population mean is given by:

   u = E(X) = sum ( x* P(x) )

      = 25*0.2 + 40*0.5 + 65*0.3

      = 44.5      

- The probability distribution of  s ^2:

        s^2  =            0                112.5                 312.5                   800

 P ( s^2 )  =          0.38             0.20                 0.30                    0.12

         

- Expected value of s^2:

E ( s^2 ) = sum ( s^2*p ( s^2 ) )

              = 0*(0.38) + 112.5*(0.02) + 312.5*(0.30) + 800*(0.12)

              = 212.25

- The population standard deviation is given by:

   б^2 = E(X^2) -  [E(X)]^2

          = 25^2*0.2 + 40^2*0.5 + 65^2*0.3 - 44.5^2

          = 2192.5 - 1980.25

          = 212.25

- Hence, E(S2) =  б^2 = 212.25

   

                 

You might be interested in
Which expression is equivalent to (f g) (5)?
lana66690 [7]
This is an expression equivalent to the problem (f g) (10)
4 0
3 years ago
Read 2 more answers
What is the difference between an irrational number and an integer? (PLZ HELP ME ANSWER ASAP!!!! All help is appreciated! :D)
enot [183]
So, first off it would help if you could define the terms irrational number and integer. Well, an irrational number is basically any real number that can't be expressed as a ratio of integers. They also cannot be represented by terminating or continuing decimals. And an integer is pretty much any number that cannot be written as a fraction or decimal, such as -2, 13, 257. It is not 2 and 1/2, or 4.75. Those would not be integers. Do you think you can figure out the difference?

8 0
3 years ago
Help me please thank you
Arturiano [62]

Answer:Third one


Step-by-step explanation:


4 0
3 years ago
P → q is false and p is true.
arlik [135]

Answer:

False??????..........

5 0
3 years ago
Identify the range of the fuction shown in the graph
Viefleur [7K]

The answer would be B. -2 < x < 2 because if you look at the graph, the range would be left and right. So, the farthest to the left would be -2 and the farthest to the right would be 2.

It wouldn't be all real numbers.

<em>Hope this helps! - from peachimin</em>

7 0
3 years ago
Other questions:
  • A collection of nickels and dimes is worth $ 9.45. If the number of dimes is doubled, the value is $16.65. How many dimes and ho
    8·1 answer
  • The weight Wkg of a metal bar varies jointly
    12·1 answer
  • NEED HELP NOW
    7·1 answer
  • 8. John is four times as old as his son. I John is 44 years old, how old is his son?
    6·2 answers
  • Solve: 2(2x + 5) = 24<br> Enter your answer as a decimal, rounded to the nearest hundredth
    11·1 answer
  • Solving systems of equations has been used consistently throughout this course in order to shed light on all kinds of different
    6·1 answer
  • What is the value of y when X=10?
    5·1 answer
  • 9|r-2|-10&lt;-73<br> any one can solve
    5·1 answer
  • I need help with this I'm confused I need an exact answer please I will give the brainliest promise.
    14·2 answers
  • All of the following are equivalent except _____.<br><br> 1.25<br> 12.5%<br> 5 over 4 <br> 125%
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!