One normally distributed with mean value 20 in. and standard deviation .5 in. The length of the second piece is a normal rv with mean and standard deviation 15 in. and .4 in., respectively. The amount of overlap is normally distributed with mean value 1 in. and standard deviation .1 in. Assuming that the lengths and amount of overlap are independent of each other, what is the probability that the total length after insertion is between 34.5 and 35 in.

Answers

Answer 1

Answer:

Answer:

The probability that the the total length after insertion is between 34.5 and 35 inches is 0.1589.

Step-by-step explanation:

Let the random variable X represent the length of the first piece, Y represent the length of the second piece and Z represents the overlap.

It is provided that:

$X\sim N(20,\ 0.50^(2))\nY\sim N(15,\ 0.40^(2))\nZ\sim N(1,\ 0.10^(2))$

It is provided that the lengths and amount of overlap are independent of each other.

Compute the mean and standard deviation of total length as follows:

$E(T)=E(X+Y-Z)\n=E(X)+E(Y)-E(Z)\n=20+15-1\n=34$

$SD(T)=√(V(X+Y-Z))\n=√(V(X)+V(Y)+V(Z))\n=\sqrt{0.50^(2)+0.40^(2)+0.10^(2)}\n=0.6480741\n\approx 0.65$

Since X, Y and Z all follow a Normal distribution, the random variable T, representing the total length will also follow a normal distribution.

$T\sim N(34, 0.65^(2))$

Compute the probability that the the total length after insertion is between 34.5 and 35 inches as follows:

$P(34.5<T<35)=P((34.5-34)/(0.65)<(T-\mu_(T))/(\sigma_(T))<(35-34)/(0.65))\n\n=P(0.77<Z<1.54)\n\n=P(Z<1.54)-P(Z<0.77)\n\n=0.93822-0.77935\n\n=0.15887\n\n\approx 0.1589$

*Use a z-table.

Thus, the probability that the the total length after insertion is between 34.5 and 35 inches is 0.1589.

Related Questions

The sum of three consecutive numbers is 318. What is the third number in the series?
You have also set up a card game in which a player picks a card from a standard deck of 52 cards. The player wins if these two events occur together: E1, in which the card drawn is a black card, and E2, in which the card drawn is a numbered card, 2 through 10.What is the probability of getting a black card and a numbered card? Calculate the probabilities P(E1) and P(E2) as fractions.
In Exercise, solve the equation.ex– 1 = 9
The value of 33 + 42 = .
Square root of -61 to the nearest tenth

What is the equation of the line? Y= 1/2x + 2

Y= 2x + 2

Y= 2x - 4

Y = 1/2x - 4

Answers

Answer:

y=1/2x+2

Step-by-step explanation:

Which equation represents the polar form of x2 + (y + 4)2 = 16?

Answers

The polar form of equation is r = -8sinθ.

What is polar form of complex number?

The combination of the complex number's modulus r and argument is how complex numbers are shown in polar form z = r cosθ + i r sinθ = r (cosθ + i sinθ), is the polar form of a complex number with coordinates (x, y). In the coordinate system, polar coordinates of real and imaginary numbers are used to represent the polar form.

Given x² + (y + 4)² = 16

here The following is the relationship between (r, θ) and (x, y) if they are in Cartesian form:

x = rcosθ, y = rsinθ and r² = x² + y² ad tanθ = y/x

x² + (y + 4)² = 16

x² + y² + 16 + 8y = 16

x² + y² + 8y = 0

r² + 8rsinθ = 0

r(r + 8sinθ) = 0

r =0 and r = -8sinθ

Hence the polar form of equation is r = -8sinθ.

Learn more about polar form of complex number;

brainly.com/question/24245821

#SPJ2

Answer:

c. r=-8sin(theta)

Step-by-step explanation:

edge 2021

Please help ! Thanks

Answers

Answer: 12x - 24y - 2

Step-by-step explanation:

Answer:

12x-24y-2

Step-by-step explanation:

So, we multiple all the values in the bracket with six to get something like this:

$(6*2x)+(6*-4y)+(6*-(1)/(3) )\n= 12x + (-24y) + (-2)\n= 12x -24y -2$

-2 1/2 x (-1 2/3) what is the answer for this question

Answers

Answer: 4 1/6

Step-by-step explanation:

An investment company advertised that last year its clients, on average, made a profit of 8% . Assuming that average refers to the mean, which of the following claims must be true based on this information?a. This year some of their clients will make a profit of at least 8%.
b. Last year some of their clients made a profit of at least 8%.
c. Last year more than half of their clients made a profit of at least 8%.
d. Last year at least one of their clients made a profit of more than 11%.
e. Last year at least one of their clients made a profit of exactly 8%.
f. None of the above statements is true.

Answers

Answer:

The answer is "Option 2".

Step-by-step explanation:

Please find the complete question in the attached file.

When there is a mean value k in a set of data. Otherwise, we will assert with certainty that at least one of the values is k. They can't say anything at all about the maximum or even the minimum using knowledge only. Nevertheless, we know that certain numbers cannot be over and that all numbers cannot be below than mean. Mean also no value throughout the data set must be equal.

Final answer:

None of the claims must necessarily be true based on the 8% average profit data provided. The information supplied does not specify individual profits, future profits, or the distribution of profits.

Explanation:

Based on the statement that the investment company's clients on average, made a profit of 8% last year, none of the claims must necessarily be true. The key phrase here is that the average profit was 8% - this does not provide specific information about any individual client's profit.

Option a is not necessarily true because this statement makes assumptions about future profits, which cannot be ascertained from last year’s average profit. For option b: even if the average profit was 8%, it's possible that no single client made exactly 8%. Similar logic applies to option c. The average doesn't tell us the distribution of the data, so we cannot deduce that more than half the clients made a profit of at least 8%. For option d: we cannot confirm if at least one client made a profit of more than 11% purely based on the average profit figure of 8%. Lastly, for option e: it's possible, but not guaranteed, that at least one client made a profit of exactly 8%. Hence, the answer is option f: None of the above statements is true.