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
7. Which pair shows equivalent expressions? A. 3(x+2) = 3x + 6 B. 3x + 2x = x²(x + 2) C. 3x + 2 = 3(x + 2) D. -3(2 + x) = -6x -
Sergio039 [100]
C has equivalent expressions I think
8 0
2 years ago
What is the trigonometric ratio for cos D ?
leva [86]

Answer:

Here,

  • H=75
  • P=72
  • B=21

We know that cosD= b/h

=21/75

=7/25

7 0
2 years ago
Can you please explain how you did it. Thanks!
vivado [14]
Well first you would start by setting up with a proportion.
In total, the girls paid $54+$22= $76
Thus 1 sister contributed $54/$76=x/100
The other sister contributed $22/$76=x/76
For each proportion, cross-multiply and simplify to get the percentage. The percentage will be the x
5 0
3 years ago
Read 2 more answers
The formula to find the perimeter of a rectangle is: P = 2W + 2L. To solve for " W " in this formula, which steps should be foll
netineya [11]
Since the 2L is not being multiplied or divided, and it's positive, we will subtract it from both sides. Since the W is being multiplied by the 2, we'll also need to divide both sides by 2. 

Your answer is B.
<em>
</em><em>Don't forget to rate this answer the Brainliest!</em>

3 0
3 years ago
Read 2 more answers
Bill and his friends went to red robin. Their order consisted of 2 hamburgers to $5.49 each, a chicken sandwich for $6.25, an or
Dvinal [7]

Answer:

47.27

Step-by-step explanation:

5.49+5.49+6.25+12.99+1.75+1.75+1.75+1.75=37.22

37.22×.20 for tip=7.44

37.22×.07 for tax=2.61

37.22+7.44+2.61=47.27

6 0
3 years ago
Read 2 more answers
Other questions:
  • Use a net to find the surface area of the open cylinder with only one base. Use 3.14 for pi.
    10·1 answer
  • Prove it :
    10·1 answer
  • 55430 millimeters over centim
    11·1 answer
  • HELP ME PLEASE I NEED ITTTTTT I WILL REWARD
    12·1 answer
  • On a coordinate plane, a triangle has points (negative 5, 1), (2, 1), (2, negative 1).
    9·2 answers
  • Help ASAP! Use the graph to answer the question
    6·2 answers
  • Please answer, i will give a brainliest
    10·2 answers
  • What is 3 divided by 7 times 56 minus 45
    11·1 answer
  • Elena wants to make a scale drawing of her bedroom. Her bedroom is a rectangle with length 5 m and width 3 m. She decides on a s
    9·1 answer
  • If 4(x-3)=16, what does 8x equal
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!