Suppose X, Y, and C represent the length, width, and perimeter of a flat rectangular sheet...
Suppose X, Y, and C represent the length, width, and perimeter of a flat rectangular sheet metal part. Note that X is a normal random variable having a mean of 15 cm and a standard deviation of 1 cm, and Y is independent of X and normally distributed with a mean of 25 cm and a standard deviation of 2 cm. Determine the following. Determine Pr(C>83).
Homework Answers
Ans:
Perimeter=2X+2Y
Distribution for C:
mean=2*15+2*25=30+50=80
standard deviation=sqrt(2^2*1^2+2^2*2^2)=4.472
C is normally distributed with mean=80 and standard deviation=4.472
z=(83-80)/4.472
z=0.671
P(C>83)=P(z>0.671)=0.2512
Add Answer to:
Suppose X, Y, and C represent the length, width, and perimeter
of a flat rectangular sheet...
QUESTION 3 10 p Suppose x, Y, and C represent the length, width, and perimeter of...
QUESTION 3 10 p Suppose x, Y, and C represent the length, width, and perimeter of a flat rectangular sheet metal part. Note that X is a normal random variable having mean 35cm and standard deviation 3 cm, and Y is independent of X and normally distributed with a mean of 15 cm and a standard deviation of 4 cm. What is the probability that the perimeter is between 96 and 105 cm? ( Report answer to three decmal places....
10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean...
10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean 2 and standard deviation !5 Y has mean 5 and standard deviation 3. Their correlation is 0.6. What is the mean and standard deviation of X + Y? What is the distribution of X+ Y? What if X and Y are jointly normally distributed? What if they are not jointly normally distributed? Explain your answer.
7. Suppose that the width of pebbles in a river is normally distributed with mean of...
7. Suppose that the width of pebbles in a river is normally distributed with mean of 12.1 mm and standard deviation of 3.2 mm. a. What is the probability that X is smaller than 11? b. A random sample of 12 pebbles is taken. What is the probability that X-bar < 11?
A flat thin rectangular lamina lies in the x-y plane as shown in Figure 2. It...
A flat thin rectangular lamina lies in the x-y plane as shown in Figure 2. It has a width W and a length L. If the surface density mu = mu_0(y/L + 1): (a) What is the total mass of the lamina (ignore the thickness T of the object). (b) Where is the centre-of-mass located on the object?
5) The figure below illustrates a large, flat, metal rectangular plate having large length, L (measured...
5) The figure below illustrates a large, flat, metal rectangular plate having large length, L (measured along the x-axis), large width, W (measured along the y-axis), and small thickness T (measured along the z-axis). Current I flows through the plate with uniform current density (directed along the positive x-axis) a) Use a symmetry argument to determine the direction of the magnetic field near the center of the plate at a field point, which is a distance z above the geometric...
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X +...
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X + Y - Z is a random variable with mean 0 and variance 2, but not necessarily normal distributed. a normal random variable with mean 0 and variance 4. O a random variable with mean 0 and variance 4, but not necessarily normal distributed. a random variable with mean 0 and variance 6, but not necessarily normal distributed. a normal random variable with mean 0...
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X +...
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X + Y - Z is a random variable with mean 0 and variance 2, but not necessarily normal distributed. a normal random variable with mean 0 and variance 4. O a random variable with mean 0 and variance 4, but not necessarily normal distributed. a random variable with mean 0 and variance 6, but not necessarily normal distributed. a normal random variable with mean 0...
Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2...
Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2 and X is another normally distributed random variable with μ-: 5 and σ-5. Y and X are independent. Calculate the following probabilities according to a normal distribution table (e.g., a normal table found from the Internet) (1) (4 points) Pr(Y> 12) (2) (4 points) Pr(2 < X <4) (3) (4 points) Pr(Y> 12 and 2< X <4) and Pr(Y> 12 or 2< X <4)...
Question 5 - Even More Fun With Bivariate Normal Distributions Let X and Y be independent normall...
Question 5 - Even More Fun With Bivariate Normal Distributions Let X and Y be independent normally distributed with mean x = 2 and μΥ--3 and standard deviations ơX-3 and ơY-5, respectively. Determine the following: (a) P(3X 6Y>15), (b) P(3X6Y<30) (c) Cov(X, Y) d) Verify (a) and (b) using R code, where for each case you generate a million X's and a million Y's and simulate the linear combination 3X 6Y. (e) Assume now that the random variables come from...
4. In a factory, the length of a certain metal bar is normally distributed, and has...
4. In a factory, the length of a certain metal bar is normally distributed, and has a mean of 50 cm, and a standard deviation of 0.07 cm. Two bars are selected and the measurements are 50.05cm and 49.99 cm. To calculate the probability that the length falls between 50.05 and 49.99, we need to standardize the normal distribution by calculating the z- scores. What are the z-scores of the lengths of the two bars?
QUESTION 3 10 p Suppose x, Y, and C represent the length, width, and perimeter of a flat rectangular sheet metal part. Note that X is a normal random variable having mean 35cm and standard deviation 3 cm, and Y is independent of X and normally distributed with a mean of 15 cm and a standard deviation of 4 cm. What is the probability that the perimeter is between 96 and 105 cm? ( Report answer to three decmal places....
10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean 2 and standard deviation !5 Y has mean 5 and standard deviation 3. Their correlation is 0.6. What is the mean and standard deviation of X + Y? What is the distribution of X+ Y? What if X and Y are jointly normally distributed? What if they are not jointly normally distributed? Explain your answer.
7. Suppose that the width of pebbles in a river is normally distributed with mean of 12.1 mm and standard deviation of 3.2 mm. a. What is the probability that X is smaller than 11? b. A random sample of 12 pebbles is taken. What is the probability that X-bar < 11?
A flat thin rectangular lamina lies in the x-y plane as shown in Figure 2. It has a width W and a length L. If the surface density mu = mu_0(y/L + 1): (a) What is the total mass of the lamina (ignore the thickness T of the object). (b) Where is the centre-of-mass located on the object?
5) The figure below illustrates a large, flat, metal rectangular plate having large length, L (measured along the x-axis), large width, W (measured along the y-axis), and small thickness T (measured along the z-axis). Current I flows through the plate with uniform current density (directed along the positive x-axis) a) Use a symmetry argument to determine the direction of the magnetic field near the center of the plate at a field point, which is a distance z above the geometric...
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X + Y - Z is a random variable with mean 0 and variance 2, but not necessarily normal distributed. a normal random variable with mean 0 and variance 4. O a random variable with mean 0 and variance 4, but not necessarily normal distributed. a random variable with mean 0 and variance 6, but not necessarily normal distributed. a normal random variable with mean 0...
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X + Y - Z is a random variable with mean 0 and variance 2, but not necessarily normal distributed. a normal random variable with mean 0 and variance 4. O a random variable with mean 0 and variance 4, but not necessarily normal distributed. a random variable with mean 0 and variance 6, but not necessarily normal distributed. a normal random variable with mean 0...
Problem 1 (16 points). Suppose that Y is normally distributed random variable with u-10 and σ-2 and X is another normally distributed random variable with μ-: 5 and σ-5. Y and X are independent. Calculate the following probabilities according to a normal distribution table (e.g., a normal table found from the Internet) (1) (4 points) Pr(Y> 12) (2) (4 points) Pr(2 < X <4) (3) (4 points) Pr(Y> 12 and 2< X <4) and Pr(Y> 12 or 2< X <4)...
Question 5 - Even More Fun With Bivariate Normal Distributions Let X and Y be independent normally distributed with mean x = 2 and μΥ--3 and standard deviations ơX-3 and ơY-5, respectively. Determine the following: (a) P(3X 6Y>15), (b) P(3X6Y<30) (c) Cov(X, Y) d) Verify (a) and (b) using R code, where for each case you generate a million X's and a million Y's and simulate the linear combination 3X 6Y. (e) Assume now that the random variables come from...
4. In a factory, the length of a certain metal bar is normally distributed, and has a mean of 50 cm, and a standard deviation of 0.07 cm. Two bars are selected and the measurements are 50.05cm and 49.99 cm. To calculate the probability that the length falls between 50.05 and 49.99, we need to standardize the normal distribution by calculating the z- scores. What are the z-scores of the lengths of the two bars?
Most questions answered within 3 hours.
-
Little’s Law: Val d’Costa is a world famous ski village in the
French Alps. Because of...
asked 5 minutes ago -
Find the absolute error D for the calculation if A + B/C=D A=
9.4 +/- 0.4...
asked 18 minutes ago -
New Air Heating and Cooling, manufactures furnaces and central
air units. The company pride itself on...
asked 32 minutes ago -
A coach uses a new technique to train gymnasts. Seven
gymnasts were randomly selected and their...
asked 2 hours ago -
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 4 hours ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 6 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 6 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 8 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 8 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 8 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 8 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 8 hours ago