The U.S. government has devoted considerable funding to missile defense research over the past 20 years. The latest development is the Space-Based Infrared System (SBIRS), which uses satellite imagery to detect and track missiles (Chance, Summer 2005). The probability that an intruding object (e.g. a missile) will be detected on a ight track by SBIRS is 0.8. consider a sample of 20 simulated tracks, each with an intruding object. Let x equal the number of these tracks where SBIRS detects the object.

Required:
a. Demonstrate that x is (approximately) a binomial random variable.
b. Give the values of p and n for the binomial distribution.
c. Find P(x = 15), the probability that SBIRS will detect the object on exactly 15 tracks.
d. Find P(x≥15) the probability that SBIRS will detect the object on at least 15 tracks.
e. Find E(x) and interpret the result.

Answers

Answer 1

Answer:

Part A:

[tex]P(X=x)=n_{C_{x}}*p^x*(1-p)^{n-x}[/tex]

x is a binomial Random Variable.

Part B:

Value of p=0.8

Value of n=20

Part C:

P(X=15)=0.17456

Part D:

P(X≥15)=0.80417

Part E:

E(x)=16

E(x) tells us that out of 20 tracks the SBIRS will detect from 16 tracks.

Step-by-step explanation:

Part A:

Binomial Distribution is used because the number of tracks and the probability to find the intruding object is constant for all tracks

It means:

[tex]P(X=x)=n_{C_{x}}*p^x*(1-p)^{n-x}[/tex]

x is a binomial Random Variable.

Part B:

Value of p=0.8

Value of n=20

Part C:

x=15

[tex]P(X=15)=20_{C_{15}}*0.8^{15}*(1-0.8)^{20-15}\\[/tex]

By solving above Expression:

P(X=15)=0.17456

Part D:

P(X≥15)=P(X=15)+P(X=17)+P(X=16)+P(X=18)+P(X=19)+P(X=20)

[tex]P(X=15)=20_{C_{15}}*0.8^{15}*(1-0.8)^{20-15}\\[/tex]

P(X=15)=0.17456

[tex]P(X=16)=20_{C_{16}}*0.8^{16}*(1-0.8)^{20-16}\\P(X=16)=0.21819[/tex]

[tex]P(X=17)=20_{C_{17}}*0.8^{17}*(1-0.8)^{20-17}\\P(X=17)=0.20536[/tex]

[tex]P(X=18)=20_{C_{18}}*0.8^{18}*(1-0.8)^{20-18}\\P(X=18)=0.13691\\\\P(X=19)=20_{C_{19}}*0.8^{19}*(1-0.8)^{20-19}\\P(X=19)=0.05765\\\\P(X=20)=20_{C_{20}}*0.8^{20}*(1-0.8)^{20-20}\\P(X=20)=0.01153[/tex]

Now, Adding Probabilities:

[tex]P(X=15)+P(X=17)+P(X=16)+P(X=18)+P(X=19)+P(X=20)\\=0.17456+0.21819+0.20536+0.13691+0.05765+0.01153\\[/tex]

P(X≥15)=0.80417

Part E:

Mean Distribution:

E(x)=n*p

E(x)=20*0.8

E(x)=16

E(x) tells us that out of 20 tracks the SBIRS will detect from 16 tracks.


Related Questions

Teagan was playing Trouble and recorded the number
of times she rolled a 6. During the game, she was
successful 5 times out of the 25 times she tried.
What was the experimental probability of rolling a 6 in
the game? Write your answer in decimal form.

Answers

Answer:

20%

Step-by-step explanation:

Think about it. 100 divided by 25 is four so just multiply 5 times 4 and you got 20. giving you the probability of 20%. Your Welcome! And I'm not a genius it's just simple math.

I posted 2 question of this but nobody answered first answer gets brainliest and a thanks and 5 stars and 20 points and do all of them or half no links ASAP guessers will be reported

Answers

Answer:

14. 13.65

15. 7.53

17. 0.0371

18. 0.81

19. 0.864

Here are some answers! Hope this helps

I'm really stuck and need help asap. ​

Answers

a = 8

b = 1/4

c = 1

hope this helped :)

Answer:

ax= 8x, by=1/4y and c=1 try that

please soleeeeeeeeeeeeèeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee​

Answers

Step-by-step explanation:

Answer is 99. I am pretty sure.

Find the 12th term of the geometric sequence 5, –25, 125, ...
HELP ASAP WILL NAME BRAINLEST

Answers

Step-by-step explanation:

[tex]U _{ {12}^{th} } = a {r}^{(n - 1)} \\ = 5 \times {5}^{12 - 1} \\ = 244140625 \\ {12}^{th} \: term \: is \: 244140625[/tex]

What is 24 – 6х3+52 - (16+ 2)?
ОА.
9
ОВ.
23
Ос.
71
OD.
496

Answers

Answer:

40

Step-by-step explanation:

24 – 6х3+52 - (16+ 2)

PEMDAS states we do the paranthesis 1st

24 – 6 х 3 + 52 - (18)

Next, we do the multiplication

24 - 18 + 52 - 18

Since it's just adding & subtracting, we go from left to right

40

multiplying and simplify radicals!

if u get it right I’ll give brainliest (show math pls!!!)

I would rlly appreciate it if y’all help me! :)

Answers

Answer:

10√5 - 5√2

or

5(2√5 - √2)

Step-by-step explanation:

Given:

2√5(5 - 5√5)

Required:

Multiply and simplify

Solution:

2√5(5 - 5√5)

Apply distributive property by multiplying each term in the bracket by 2√5

2√5*5 - 2√5*5√5

2*5√5 - 2*5√5*√5

10√5 - 10√25

10√5 - 10*5

10√5 - 50

10√5 - (25*2)

10√5 - 5√2

Or

5(2√5 - √2)

Choose the sentence that is out of sequence.

Mary Jo began reading The Alphabet Book.
Mother put Jimmy to bed.
Jimmy helped read.
Jimmy fell asleep.

Answers

Answer:

C.

Step-by-step explanation:

Ms.schmidt gav her students the list of number shown below

Answers

Step-by-step explanation:

Can you re-do it and send like an example for it THANK YOU SM

Four friends were born in consecutive years. The sum of their ages is 62.
What is the age of the oldest friend?

Answers

Answer:

4+62=66

Step-by-step explanation:

I need help with this

Answers

Answer:

cool dude

Step-by-step explanation:

1/2x+8=20 what does x equal

Answers

Answer:

x=24

Step-by-step explanation:

1/2 x + 8 =20

x/2 + 8= 20

X is equal to 24

24= x


A pair of weak earthquakes is modeled by a system of inequalities. One earthquake occurred roughly 20 km east and 14 km north of the center of Columbia, NC. The quake could be felt from 25 km away. A couple days later, another earthquake occurred 8 km west and 3 km north of the center of Columbia and could be felt from 14 km away. If Columbia is located at (0, 0) on a coordinate grid, the system of inequalities represents this scenario.

StartLayout Enlarged left-brace first row (x minus 20) squared + (y minus 14) squared less-than-or-equal-to 625 second row (x + 8) squared + (y minus 3) squared less-than-or-equal-to 196 EndLayout

Which location relative to Columbia felt both earthquakes?

4 km west and 12 km south
6 km west and 4 km north
2 km east and 10 km north
6 km east and 8 km north

Answers

Answer:

2 km east and 10 km north

Step-by-step explanation:

I did the activity and got the right answer.

By evaluating the inequalities, we will see that the correct option is: 2 km east and 10 km north

Which location will feel both earthquakes?

Here we have the inequalities:

(x - 20)^2 + (y - 14)^2 ≤ 625

(x + 8)^2 + (y - 3)^2 ≤ 196

Where, x is the distance due east, and y is the distance due north.

So we just need to find which of the given options makes both inequalities true, for example, for the first one we have:

x = -4

y = -12

Replacing that on the first inequality we get:

(-4 - 20)^2 + (-12 - 14)^2 ≤ 625

1,252 ≤ 625

This is false, so this option is not correct.

Now we just need to check the other options. Particularly for the third we have:

x = 2

y = 10

Replacing that in both inequalities we get:

(2 - 20)^2 + (10 - 14)^2 ≤ 625

340 ≤ 625 (true).

(2 + 8)^2 + (10 - 3)^2 ≤ 196

149 ≤ 196 (true)

So at 2km east and 10km north of Columbia, the two earthquakes can be felt.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/18881247

HELP WILL GIVE BRAINLIEST!

Answers

Answer:

128 boxes

Step-by-step explanation:

The dimensions of the trunk is 24 in. by 24 in by 48 in

The volume = 24(24)(48) = 27648 cu. in.

The cubed boxes each have a volume of 6(6)(6) = 216 cu. in.

27648/216 = 128 boxes

Frederick's salary varies directly with the hours he works. Last week I earned $ 328.30 and worked 33.5 hours. If he works 35 hours this week, what will be his salary from him?

Answers

Answer:

His salary will be of $343.

Step-by-step explanation:

Frederick's salary varies directly with the hours he works.

This means that this question can be solved by proportions, using a rule of three.

We have that:

For 33.5 hours, he earned $328.30. How much he earns for 35 hours?

33.5 hours - $328.30

35 hours - $x

Applying cross multiplication:

[tex]33.5x = 328.30*35[/tex]

[tex]x = \frac{328.30*35}{33.5}[/tex]

[tex]x = 343[/tex]

His salary will be of $343.

Which situation can be modeled by the expression 4 divided 1/3

Answers

4 jar is the correct answer to the question

Answer:

4

Step-by-step explanation:

4/1x 3/1 =12/1=4

In the triangle below,
x = [? ] cm. Round to the
nearest tenth.
y
X
90°
20
10 cm
X=?

Answers

Answer: y ≈ 10.6 cm

Step-by-step explanation:

The cosine function relates the adjacent side to the hypotenuse in a right triangle. The side adjacent to the 20° angle is 10 cm.

cos(20°) = (10 cm)/y

y = (10 cm)/cos(20°)

y ≈ 10.6 cm

The approximate value of the variable x will be 3.64.

What is a right-angle triangle?

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The base of the right angle triangle is 10 cm, the perpendicular is x, and the hypotenuse is y.

Then the value of y will be given by the cosine of angle 20°.

cos 20° = 10/y

          y = 10.64 cm

The approximate value of the variable x is given by the Pythagoras theorem.

     H² = P² + B²

10.64² = x² + 10²

113.25 = x² + 100

      x² = 113.25 – 100

      x² = 13.25

       x = 3.64

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In a display at a museum, two planets have volumes of 8 cubic inches and 27 cubic
inches. What is the ratio of their diameters?
2:3
413.5
2:9
4:13.5

Answers

Answer:

2:3

Step-by-step explanation:

V = 4/3*pi*r^3

Diameter = 2r

The ratio of diameters of the two planets has volumes of 8 cubic inches and 27 cubic will be 2/3.

What is Ratio?

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other such that they should not be divisible.

The upper number is called as the numerator and the lower is called the denominator.

For example, 3/4 where 3 will be numerator and 4 will be denominator.

Given that the In a display at a museum, two planets have volumes of 8 cubic inches and 27 cubic.

Now volume of planets(sphere) = πD³/6 where D is diameter of sphere

So volume of first planet / volume of second planet ∝ (dia or first)³/(dia of second)³

⇒ V₁/V₂  ∝ (D₁/D₂)³

Given that V₁/V₂ = 8/27

So 8/27 =  (D₁/D₂)³

D₁/D₂ = 2/3

Hence, the ratio of diameters of two planets will be 2/3.

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Which of the following values is not changed by moving the center of an ellipse? a or b b c a, b or c

Answers

Answer:

a, b or c

Step-by-step explanation:

Giving the brainliesttt
What is the range when the domain is
A) -8
B) -4
C) 4
D) 0
E) 10

Answers

It A -8 is the answer

Match the appropriate transformation with the appropriate rule.

Answers

Answer:

i only know one, which is c and 2

Step-by-step explanation:

Math people please answer me this please fast!!!!!

Answers

Answer:

Wait nvm sorry point A is at (1,-5) so the answer is B

Step-by-step explanation:

write an equation of the line that passes through the given points (-1,3.5),(1,-0.5), (3,-4.5)

Answers

Yo⁣u ca⁣n downloa⁣d th⁣e answe⁣r her⁣e

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer:

y = -2x + 1.5

Step-by-step explanation:

line that passes through the given points (-1,3.5),(1,-0.5), (3,-4.5)

slope (m) = (-0.5 - 3.5) / (1 - -1) = -4 / 2 = -2

(y - -4.5) / (x - 3) = -2   ... pass (3,-4.5)

y + 4.5 = -2x +6

y = -2x + 1.5

Which function represents a quantity growing exponentially?


A y = 2(0.5)

В y = 0.5(2)

C y = 2(0.5)2X

D y = 6)​

Answers

Answer: c

Step-by-step explanation:

A parachutist's speed during a free fall reaches 180 kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 2 seconds of free fall? Do not round your answers. Speed: 50ms Distancefallenin2seconds: 1,000m

pls hurry exam

Answers

Answer:

Speed of the parachutist is meters per second [tex]2.083[/tex] meter per second

Distance travelled in 2 seconds [tex]4.167[/tex] meter

Step-by-step explanation:

Speed of the parachutist is kilometers per hour = 180

Speed of the parachutist is meters per second [tex]\frac{180*1000}{24*60*60} = 2.083[/tex] meter per second

Distance travelled in 2 seconds [tex]2.083 *2 = 4.167[/tex] meter

A line is parallel to the line y=-2/3x+1 and it passes through the point (4,-1). Determine the slope of the line.
A) m=2/3
B)m=-3/2
C)m=-2/3
D)m= 3/2

Answers

Answer:

C) m=-2/3

Step-by-step explanation:

Parallel slope means it'll be the same.

m = -2/3

Can someone pleaseeee help me

Answers

Answer:

a). Common difference = 4

b). [tex]T_n=4n+3[/tex]

c). 51st term = 207

Step-by-step explanation:

Given arithmetic sequence is,

7, 11, 15, 19......

a). Common difference = Second term - First term

                                      = 11 - 7

                                      = 4

b). nth term of an arithmetic sequence is given by,

   [tex]T_n=a+(n-1)d[/tex]

   Here, n = number of term

   a = First term

   d = common difference

   By substituting the values in the given formula,

   [tex]T_n=7+(n-1)4[/tex]

   [tex]T_n=4n+3[/tex]

c). 51st term of the sequence will be,

   [tex]T_{51}=7+(51-1)4[/tex]

         = 7 + 200

         = 207

Helppppp! What is the value of 5^3i^9

Answers

Answer:

125i.

Step-by-step explanation:

5^3 is 125 i^2 is -1 so i^8 is positive and you have 1 i left.

graph the function y=x3+3x2-1. based on the graph what is the least possible x-value if y=0? round your answer to the nearest hundredth, if necessary

o -2.88
o -2.00
o -0.65
o -0.53

Answers

Answer:

-2.88

Step-by-step explanation:

When graphed Y=0 crosses the X-axis three times

X= -2.88, -0.65, 0.53

Answer:

It's A on edge or -2.88

Step-by-step explanation:

write a quadratic equation in the form x^2+bx+c=0 that has the following roots: {-7,6}

Answers

Answer:

f(x) = x^2 -12x + 85

reverse engineer this, like Prof. Sheldon Cooper figuring out Howard's card trick

x=6+or - 7i

x-6 = + or - 7i

square both sides

(x-6)^2 = -49

x^2 -12x + 36 = -49

x^2 -12 + 85

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