Mathematics, 26.03.2020 20:08 mikki93

Suppose the expected tensile strength of type-A steel is 103 ksi and the standard deviation of tensile strength is 7 ksi. For type-B steel, suppose the expected tensile strength and standard deviation of tensile strength are 105 ksi and 5 ksi, respectively. Let X^- = the sample average tensile strength of a random sample of 80 type-A specimens, and let Y^- = the sample average tensile strength of a random sample of 60 type-B specimens.
a. What is the approximate distribution of X^-? Of Y^-?
b. What is the approximate distribution of (X^-) - (Y^-)? Justify your answer.
c. Calculate (approximately) P(-1<_ X^- - Y^- <_1)

Answers: 1

Show answers

Answers

Answer from: gokusupersaiyan12345

i So the approximate distribution of $\= X$ is $\mu_{\= X} =103$ and $\sigma_{\= X} = 0.783$

ii So the approximate distribution of $\= Y$ is $\mu_{\= Y} =105$ and $\sigma_{\= Y} = 0.645$

the approximate distribution of $\=X - \= Y$ is $E (\= X - \= Y) = -2$ and $\sigma_{\= X - \=Y}=1.029$

Here we can see that the mean of the approximate distribution is negative which tell us that this negative value of the data for $\=X - \= Y$ sample are more and their frequency occurrence is higher than the positive values

the value of $P(-1 \le \=X - \= Y \le 1)$ is = -0.1639

Step-by-step explanation:

From the question we are given that

The expected tensile strength of the type A steel is $\mu_A = 103 ksi$

The standard deviation of type A steel is $\sigma_A = 7ksi$

The expected tensile strength of the type B steel is $\mu_B = 105\ ksi$

The standard deviation of type B steel is $\sigma_B = 5 \ ksi$

Also the assumptions are

Let $\= X$ be the sample average tensile strength of a random sample of 80 type-A specimens

Here n_a =80

Let $\= Y$ be the sample average tensile strength of a random sample of 60 type-B specimens.

Here n_b = 60

Let the sampling distribution of the mean be

$\mu _ {\= X} = \mu$

=103

Let the sampling distribution of the standard deviation be

$\sigma _{\= X} = \frac{\sigma }{\sqrt{n_a} }$

$= \frac{7}{\sqrt{80} }$

=0.783

So What this mean is that the approximate distribution of $\= X$ is $\mu_{\= X} =103$ and $\sigma_{\= X} = 0.783$

For $\= Y$

The sampling distribution of the sample mean is

$\mu_{\= Y} = \mu$

= 105

The sampling distribution of the standard deviation is

$\sigma _{\= Y} = \frac{\sigma }{\sqrt{n_b} }$

$= \frac{5}{\sqrt{60} }$

= 0.645

So What this mean is that the approximate distribution of $\= Y$ is $\mu_{\= Y} =105$ and $\sigma_{\= Y} = 0.645$

Now to obtain the approximate distribution for $\=X - \= Y$

$E (\= X - \= Y) = E (\= X) - E(\= Y)$

$= \mu_{\= X} - \mu_{\= Y}$

= 103 -105

= -2

The standard deviation of $\=X - \= Y$ is

$\sigma_{\= X - \=Y} = \sqrt{\sigma_{\= X}^2 - \sigma_{\= Y}^2}$

$= \sqrt{(0.783)^2 + (0.645)^2}$

=1.029

Now to find the value of $P(-1 \le \=X - \= Y \le 1)$

Let us assume that $F = \= X - \= Y$

$P(-1 \le F \le 1)$ $= P [\frac{-1 -E (F)}{\sigma_F} \le Z \le \frac{1-E(F)}{\sigma_F} ]$

$= P[\frac{-1-(-2)}{1.029} \le Z \le \frac{1-(-2)}{1.029} ]$

$= P[0.972 \le Z \le 2.95]$

$= P(Z \le 0.972) - P(Z \le 2.95)$

Using the z-table to obtain their z-score

= 0.8345 - 0.9984

= -0.1639

Answer from: Quest

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

Answer from: Quest

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17

(me 30 pts: s.o.s asap) the data modeled by the box plots represent the battery life of two differ

Another question on Mathematics

Mathematics, 21.06.2019 16:30

Jackie purchased 3 bottles of water and 2 cups of coffee for a family for $7.35. brian bought 4 bottles of water and 1 cup of coffee for his family for $7.15. how much does each bottle of water cost? how much does each cup of coffee cost? i need this done

Answers: 3

Answer

Mathematics, 21.06.2019 16:40

One of the inventors of integrated circuits observed that the number of transistors that fit on an integrated circuit will double every 24 months. what type of relationship most appropriately models this situation?

Answers: 3

Answer

Mathematics, 21.06.2019 17:00

Twice the sum of a number and 4 is equal to three times the difference of the number and 7. find the number.

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Which table shows a proportional relationship between miles traveled and gas used?

Answers: 2

Answer

You know the right answer?

Suppose the expected tensile strength of type-A steel is 103 ksi and the standard deviation of tensi...