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Samples of size n = 90 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the variance is found for each sample. What is the distribution of the sample variances?

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Answer:

chi square distribution with df = n-1

Step-by-step explanation:

Given that sample of size n=90  are randomly selected from the population of numbers (0 through 9) produced by a random-number generator

Since sample size is large and randomness is followed we can assume that the variable follows a normal distribution.

Hence the sample variance would follow a chi square distribution with degree of freedom = n-1\=89

This is because we have frac{x-mu}{sigma} is standard normal hence square will be a chisquare variate.  When we sum n variates we get chi square distribution with df n-1

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In the data set, what is the variance? 6 8 1 9 4

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Answer:  [B]:  “contains one point” .
_______________________________
Explanation:
__________________
Given:
__________________
x + y  = 6  ;
x – y = 0 ;
_________________
 
To solve for “x” ;

Consider the first equation:

x + y = 6 ;

subtract “y” from each side of the equation ; to isolate “x” on one side of the equation; and to solve for “x” ;

x + y – y = 6 – y ;

x = 6 – y ;
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Take the second equation:
____________________
 x – y = 0 ;

Solve for “x” ;

Add “y” to EACH SIDE of the equation; to isolate “x” on one side of the equation; and to solve for “x” ;

x – y + y = 0 + y ;
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    x = y
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x = 6 – y

Substitute “x” for “y” ;

x = 6 – x ;

Add “x” to Each side of the equation:
_______________________________
x + x = 6 – x + x ;

2x = 6 ;

Now, divide EACH SIDE of the equation by “2” ; to isolate “x” on one side of the equation; and to solve for “x” ;

2x/2 = 6/2 ;

x = 3 .
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Now, since “x = 3” ;  substitute “3” for “x” in both original equations; to see if we get the same value for “y” ;
_______________________________
x + y  = 6  ;
x – y = 0
________________________________
Start with the first equation:
________________________________
x + y = 6 ;

3 + y = 6 ;

Subtract  “3” from each side of the equation; to isolate “y” on one side of the equation; and to solve for “y” ;

3 + y – 3 = 6 – 3 ;

y = 3 .
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Now, continue with the second equation; {Substitute “3” for “x” to see the value we get for “y”} ;
________________________
The second equation given is:
________________________
x – y = 0 ;

Substitute “3” for “x” to solve for “y” ;

3 – y = 0 ;

Subtract “3” from EACH side of the equation:

3 – y – 3 = 0 – 3 ;

      -1y = -3  ;

Divide EACH side of the equation by “-1” ;  to isolate “y” on one side of the equation; and to solve for “y” ;

-1y/-1 = -3/-1 ;

    y = 3 .
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So, for both equations, we have one value:  x = 3, y = 3;  or:  write as: 
“(3, 3)” ;  { which is:  “one single point” ;  which is:  Answer choice:  [B] } .
__________________________________________________________ 

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It is desired to estimate the mean gpa of each undergraduate class at a large university. assume that the variance of the gpas is 1.44. how large a sample is necessary to estimate the mean gpa within 0.25 at the 99% confidence level

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Mahtematical and statistical reasoning makes it evident that there is a mistake in the writing of the question and the digits were duplicated. So the right question is:

“You need to have a password with 5 letters followed by 3 odd digits between 0 and 9, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your passwor?”

The solution is:

5 letters from 26 with no repetition => 26*25*24*23*22 different choices.

odd digits are 1, 3, 5, 7 and 9 => 5 different digits to choose

3 digits from 5 with no repetition => 5*4*3 = 60

Then, the total number of choices is: 26*25*24*23*22*60 = 473,616,000

Answer: 473,616,000 choices.

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It has been reported that 63% of adults aged 65 and older got their flu shots last year. in a random sample of 300 adults aged 65 and over, find the mean, the variance, and standard deviation for the number who got their flu shots.

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It has been reported that 63% of adults aged 65 and older got their flu shots last year. in a random sample of 300 adults aged 65 and over, find the mean, the variance, and standard deviation for the number who got their flu shots.

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Find the​ mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n equals 123n=123​, p equals 0.85

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Answer:

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

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Brian collects a set of 20 data representing the lengths of worms he found in the garden. The variance of measurments is 36. What is the standard deviation from the mean?

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Ur points are set up like this (x,y)….so ur x axis number, then ur y axis number…so 2 of the points that are on ur line are (0,12000) and (120,0)
u do not subtract 2000 by 4000…if u wanted to use those points, they would be (80,4000) and (100,2000)

slope (rate of change) = (y2 – y1) / (x2 – x1)
(0,12000) …x1 = 0 and y1 = 12000
 (120,0) ……x2 = 120 and y2 = 0
slope = (0 – 12,000) / (120 – 0) = -12,000/120 = -100 <== ur slope

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The following table shows the probability distribution for a discrete random variable. X 11 14 16 19 21 23 24 29 P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08 The mean of the discrete random variable X is 18.59. What is the variance of X? Round your answer to the nearest hundredth.

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Easy way is to list multipules of 6
6,12,18,24,30,36,42,48,54
so we can see that A doesn’t work because 20 doesn’t have 6 as a common factor
C works
D doesn’t work because of the 56

answers are B and C

another way is to factor each
notice that 6=2*3
so factor each and see if we can find a 2*3 in each

A.
12=2*2*3, so there is a 6
20=2*2*5, not 6

B.
18=2*3*3, so there is a 6
24=2*2*3*3, so there is a 6
works

C.
30=2*3*5, there is a 6
54=2*3*3*3, there is a 6
works

D.
42=2*3*7, there is a 6
56=2*2*2*7, there isn’t a 6
nope

answes are B and C

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