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
deff fn [24]
3 years ago
15

A shipping company handles containers in three different sizes: (1) 27 ft3 (3 × 3 × 3), (2) 125 ft3, and (3) 512 ft3. Let Xi (i

= 1, 2, 3) denote the number of type i containers shipped during a given week. With μi = E(Xi) and σi2 = V(Xi), suppose that the mean values and standard deviations are as follows:
μ1 = 230 μ2 = 240 μ3 = 120
σ1 = 11 σ2 = 12 σ3 = 7

Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped.
Mathematics
1 answer:
GuDViN [60]3 years ago
6 0

Answer:

Expected value of the total volume shipped = 97,650 ft³

Variance of the total volume shipped = 15,183,265

Standard deviation = 3896.6 ft³

Step-by-step explanation:

The mean of number of type 1, 2 and 3 containers in a week

μ₁ = 230, μ₂ = 240, μ₃ = 120

The standard deviations for the number of type 1, 2 and 3 containers in a week

σ₁ = 11, σ₂ = 12, σ₃ = 7

When independent distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

Volume of each container type

λ₁ = 27 ft³

λ₂ = 125 ft³

λ₃ = 512 ft³

Distribution of total volume shipped

= 27X₁ + 125X₂ + 512X₃

Expected value = Combined Mean = 27μ₁ + 125μ₂ + 512μ₃

= (27×230) + (125×240) + (512×120) = 590

Combined Variance = 27²σ₁² + 125²σ₂² + 512²σ₃²

= (27² × 11²) + (125² × 12²) + (512² × 7²)

= 88,209 + 2,250,000 + 12,845,056

= 15,183,265

Standard deviation = √(15,183,265) = 3896.6 ft³

Hope this Helps!!!

You might be interested in
There are two bags of marbles. One bag contains 4 yellow, 2 blue, and 10 green. The second bag contains 12 orange, 6 green, and
Furkat [3]

Answer:

Step-by-step explanation:

10+6 = 16

A is correct answer

6 0
2 years ago
Which list orders the numbers from least to greatest?
storchak [24]

Answer:

D.

Step-by-step explanation:

5 0
2 years ago
mary had $115 to spend on clothes. she found a pair of shoes for $55 and then pants for $15 each. how many pairs of pants can sh
slega [8]

Answer:

She can buy 4 pairs of pants.

6 0
3 years ago
Read 2 more answers
Find the slope of the line below. Enter your answer as a fraction or decimal. Use a slash mark (/) as the fraction bar if necess
Llana [10]

Answer:

1/4

Step-by-step explanation:

We can use the slope formula to find the slope

m = (y2-y1)/(x2-x1)

    = (2-0)/(4 - -4)

    = (2-0)/( 4+4)

    = ( 2/8)

    = 1/4

3 0
2 years ago
Read 2 more answers
Use the equation to draw a line in the graph <br><br>3 times + 2 y _&gt; - 6​
son4ous [18]

Answer:

3 times 5 times 8 = Japanese food times 62 = Volcanoes + 10⁶ = 6.79990

3 0
3 years ago
Read 2 more answers
Other questions:
  • I need help plez and thanks
    14·2 answers
  • Can -2y = -6 be written in slope-intercept form? If so, what is it?
    8·2 answers
  • The table shows ticket prices for the local minor league baseball team for fanclub members and non-members. For how many tickets
    14·2 answers
  • I NEED THIS LIKE, RIGHT NOW. THIS IS DUE AT 3:00
    13·2 answers
  • Please help me I need this done not a lot of work but please get it done with good credit for a good reward and rating!
    12·1 answer
  • Help ༎ຶ‿༎ຶ i dont get it​
    9·2 answers
  • Predict the next number in the table. cycle: 1,2,3,4,5. people told: 1,3,9,27,?​
    6·1 answer
  • The vertical position of a particle is given by the function s = t^3 - 3t^2 - 2. How far does the particle travel between t = 0
    10·1 answer
  • Please help me<br><br><br>Find the surface area and volume of this square pyramid.​
    14·1 answer
  • Comeplete the following :<br> Rx0 Do2 : (2,4) -&gt; (-4, 8) (4, -8) (-4, -8)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!