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
stellarik [79]
3 years ago
11

The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The widt

h of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. a. Determine the mean and standard deviation of the difference between the width of the casing and the width of the door. b. What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch? c. What is the probability that the door does not fit in the casing?
Mathematics
1 answer:
Vadim26 [7]3 years ago
5 0

Answer:

a) Mean = 0.125 inch

Standard deviation = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673

c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673

Step-by-step explanation:

Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)

Let the distribution of the width of the door be X₂ (μ₂, σ₂²)

The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂

when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with

Mean = Σλᵢμᵢ

λᵢ = coefficient of each disteibution in the manner that they are combined

μᵢ = Mean of each distribution

Combined variance = σ² = Σλᵢ²σᵢ²

λ₁ = 1, λ₂ = -1

μ₁ = 24 inches

μ₂ = 23 7/8 inches = 23.875 inches

σ₁² = (1/8)² = (1/64) = 0.015625

σ₂ ² = (1/16)² = (1/256) = 0.00390625

Combined mean = μ = 24 - 23.875 = 0.125 inch

Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125

Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)

This is a normal distribution problem

Mean = μ = 0.125 inch

Standard deviation = σ = 0.13975 inch

We first normalize/standardize 0.25 inch

The standardized score of any value is that value minus the mean divided by the standard deviation.

z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89

P(X > 0.25) = P(z > 0.89)

Checking the tables

P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673

c) Probability that the door does not fit in the casing

If X₂ > X₁, X < 0

P(X < 0)

We first normalize/standardize 0 inch

z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89

P(X < 0) = P(z < -0.89)

Checking the tables

P(X < 0) = P(z < -0.89) = 0.18673

Hope this Helps!!!

You might be interested in
By how many times does the surface area of a sphere differ if radius is double​
stich3 [128]

<em>If the radius of a sphere is doubled, the surface area becomes four times the original surface area.</em>

6 0
2 years ago
Read 2 more answers
Can someone help me please
Evgen [1.6K]

Answer:

7 (7/8)

Step-by-step explanation:

There

3 0
2 years ago
What is the quotient of the complex number 4-3i divided by its conjugate?
bazaltina [42]

9514 1404 393

Answer:

  0.28 -0.95i

Step-by-step explanation:

Multiply numerator and denominator by the conjugate of the denominator.

  \dfrac{4-3i}{4+3i}=\dfrac{(4-3i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{7-24i}{25}=\boxed{0.28-0.96i}

_____

<em>Additional comment</em>

If the original number is A∠β, the ratio is 1∠(2β), the square of the unit vector in the same direction as the original.

3 0
2 years ago
Solve x^2 + 5x + 6 = 0​
grigory [225]

Answer:

(x+3)(x+2)

Step-by-step explanation:

take x^2 and take it apart. so it should be (x+  ) (x+  ) then take 6 and make it so it's multipuls equal 5. ur answer should be (x+3)(x+2) or vice versa.

4 0
3 years ago
Read 2 more answers
2x^2+17x+29 divide x+6
Maslowich
I hope this helps you

7 0
3 years ago
Other questions:
  • Ben saved twenty four 10p coins and ten 20p coins<br> How much has he saved?
    15·1 answer
  • Can someone please help me ASAP❤️
    6·1 answer
  • Plz asap maxium points will mark brainliest
    9·1 answer
  • Please help ASAP!!!!
    6·1 answer
  • Question 2 (1 point)<br> How much does the prefix milli multiply the value of a base unit?
    13·1 answer
  • What is the Surface Area of this Prism?
    9·1 answer
  • Please please help me
    9·2 answers
  • Three vans can carry<br> 18 adults. How many<br> adults are in 7 vans?
    12·2 answers
  • Banana slugs can move at 17 cm per minute. if a banana slug travels for 5 hours, how far will it travel?
    9·2 answers
  • Picture shown!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!