In statistics, the middle value of an ordered set of values is called what?

Suppose the expected tensile strength of type-A steel is 103 ksi and the standard deviation of tensile strength is 7 ksi. For ty

ExtremeBDS [4]

Answer:

a

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 $\sigma_{\= Y} = 0.645$

b

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

c

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

$= 0.8345 - 0.9984$

$= -0.1639$

3 0

3 years ago

In survey 17/25 of the people surveyed have a cat. what percent of the people surveyed have a cat?

mestny [16]

Answer:

The percentage of the people surveyed that have a cat is 68%

Step-by-step explanation:

we know that

To find the percentage of the people surveyed that have a cat, multiply the given fraction by 100

so

$\frac{17}{25}*100=17*4=68\%$

7 0

3 years ago

A bag contains 5 red marbles, 3 white marbles, and 4 blue marbles. what is the probability of randomly selecting a red marble, s

Orlov [11]

Answer:

Technically it is 5/12, but as a percentage it would be 41.6666%

5 0

3 years ago

Read 2 more answers

Rena spent 6 days reading her book completing the same fraction of the book each day if she had a total of 8/9 of her book after

Artyom0805 [142]

Answer:

The fraction of the book that Rena read every day is $\frac{4}{27}$

Step-by-step explanation:

Rena spent 6 days reading her book completing the same fraction of the book every day and you want to know the fraction of the book she read each day. Knowing that Rena had a total of 8/9 of her book read after 6 days, then you simply divide the total amount of the book read during those days by 6, the number of days:

$\frac{8}{9}$ ÷6

To divide a fraction by a whole number, you must convert the whole number into a fraction, finding the reciprocal of that fraction, and multiply it by the first fraction. That is, you must find the reciprocal of the number that is after the division symbol; and then you multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol). Remember that to find the reciprocal of a number, you simply have to change the numerator and denominator of the number.

Since 6 can be considered to be a fraction equal to $\frac{6}{1}$ , by inverting the number, then you get $\frac{1}{6}$