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levacccp [35]
4 years ago
15

N testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) at which the missil

e explodes. The distance X is measured in miles and the sampling distribution of X is given by:
X 0 10 50 100
P(X) 1⁄40 1/20 1⁄10 33⁄40

Calculate the variance of this sampling distribution.

a) 27.6

b) 5138.7

c) 761.0

d) 253.7

e) 88.0

f) None of the above
Mathematics
2 answers:
natta225 [31]4 years ago
5 0

Answer:

Var(X)=E(X^2)-[E(X)]^2 =8505-(88)^2 =761.0

c) 761.0

Step-by-step explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.  

The random variable is given by this table

X | 0 | 10 | 50 | 100 |

P(X) | 1/40 | 1/20 | 1/10 | 33/40 |

In order to calculate the expected value we can use the following formula:

E(X)=\sum_{i=1}^n X_i P(X_i)

And if we use the values obtained we got:

E(X)=(0)*(\frac{1}{40})+(10)(\frac{1}{20})+(50)(\frac{1}{10})+(100)(\frac{33}{40})=88

In order to find the variance, we need to find first the second moment, given by :

E(X^2)=\sum_{i=1}^n X^2_i P(X_i)

And using the formula we got:

E(X^2)=(0)*(\frac{1}{40})+(100)(\frac{1}{20})+(2500)(\frac{1}{10})+(10000)(\frac{33}{40})=8505

Then we can find the variance with the following formula:

Var(X)=E(X^2)-[E(X)]^2 =8505-(88)^2 =761.0

And then the standard deviation would be given by:

Sd(X)=\sqrt{Var(X)}=\sqrt{761}=27.586

So then the best answer for this case is:

c) 761.0

Ganezh [65]4 years ago
4 0

Answer:

(C) 761.0

Step-by-step explanation:

This is a grouped data with the following distance and frequency of occurrence

Formula for variance = (∑ fx²/mean)- (mean)²

x = distance

f = frequency  

n = sample size

x f/n        f x²         fx     fx²  

0 1/40        1  0         0     0  

10 1/20   2 100        20     200  

50 1/10    4 2500      200     10000  

100 33/40 33 10000 3300    330000  

     

         n         ∑ fx             ∑fx²  

        40         3520     340200  

Note frequency was given as a fraction of the sample size

mean = ∑fx/n

3520/40 = 88

mean = 88

Variance = (∑fx²/mean) - (mean)²  

Variance = ( 340200/40) – (88)²

Variance = 8505 – 7744

Variance = 761.0

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Answer: The square root of π has attracted attention for almost as long as π itself. When you’re an ancient Greek mathematician studying circles and squares and playing with straightedges and compasses, it’s natural to try to find a circle and a square that have the same area. If you start with the circle and try to find the square, that’s called squaring the circle. If your circle has radius r=1, then its area is πr2 = π, so a square with side-length s has the same area as your circle if s2  = π, that is, if s = sqrt(π). It’s well-known that squaring the circle is impossible in the sense that, if you use the classic Greek tools in the classic Greek manner, you can’t construct a square whose side-length is sqrt(π) (even though you can approximate it as closely as you like); see David Richeson’s new book listed in the References for lots more details about this. But what’s less well-known is that there are (at least!) two other places in mathematics where the square root of π crops up: an infinite product that on its surface makes no sense, and a calculus problem that you can use a surface to solve.

Step-by-step explanation: this is the same paragraph The square root of π has attracted attention for almost as long as π itself. When you’re an ancient Greek mathematician studying circles and squares and playing with straightedges and compasses, it’s natural to try to find a circle and a square that have the same area. If you start with the circle and try to find the square, that’s called squaring the circle. If your circle has radius r=1, then its area is πr2 = π, so a square with side-length s has the same area as your circle if s2  = π, that is, if s = sqrt(π). It’s well-known that squaring the circle is impossible in the sense that, if you use the classic Greek tools in the classic Greek manner, you can’t construct a square whose side-length is sqrt(π) (even though you can approximate it as closely as you like); see David Richeson’s new book listed in the References for lots more details about this. But what’s less well-known is that there are (at least!) two other places in mathematics where the square root of π crops up: an infinite product that on its surface makes no sense, and a calculus problem that you can use a surface to solve.

5 0
3 years ago
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Anna007 [38]

Hey there!

The perimeter of the floor plan is 30 inches.

Perimeter is length + length + width + width, so we can do 9 + 9 + 6 + 6 = 30

The area of the floor plan is 54 inches²

Area is length x width, so we can do 9 x 6 = 54

The perimeter of the actual size is 105 feet

First, we can solve the dimensions for the actual size. We know that 2 inches = 7 feet, so we can do 7/2 and get 3.5. This means that for every 1 inch, it's 3.5 feet. Then, we multiply the dimensions by 3.5:

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Then we solve for perimeter. Perimeter is length + length + width + width, so we can do 31.5 + 31.5 + 21 + 21 = 105

The area of the actual size is 661.5 inches²

Area is length x width, so we can do 31.5 x 21 = 661.5

Hope this helps! Tell me if you need more help.

8 0
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