Assume that each time a metal detector at an airport signals, there is a 25% chance that the cause is change in the passenger's pocket. During a given hour, 15 passengers are stopped because of a signal from the metal detector. a) Find the probability that at least 3 passengers will have been stopped due to change in their pockets. b) If 15 passengers are stopped by the detector, would it be unusual for none of these to have been stopped due to change in the pocket

Answers

Answer 1

Answer:

a) 0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.

b) 0 is less than 2.5 standard deviations from the mean, so it would not be unusual.

Step-by-step explanation:

For each passenger, there are only two possible outcomes. Either they will have been stopped due to a change in the pocket, or not. Passengers are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

A measure is considered unusual if it is more than 2.5 standard deviations of the mean.

25% chance that the cause is change in the passenger's pocket.

This means that [tex]p = 0.25[/tex]

During a given hour, 15 passengers are stopped because of a signal from the metal detector.

This means that [tex]n = 15[/tex]

a) Find the probability that at least 3 passengers will have been stopped due to change in their pockets.

This is

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

So

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

[tex]P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134[/tex]

[tex]P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668[/tex]

[tex]P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.2361 = 0.7639[/tex]

0.7639 = 76.39% probability that at least 3 passengers will have been stopped due to change in their pockets.

b) If 15 passengers are stopped by the detector, would it be unusual for none of these to have been stopped due to change in the pocket

First we find the mean and the standard deviation:

[tex]E(X) = np = 15*0.25 = 3.75[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15*0.25*0.75} = 1.68[/tex]

3.75 - 2.5*1.68 = -0.45

0 is less than 2.5 standard deviations from the mean, so it would not be unusual.


Related Questions

hotel has 44 storeys Each storey has 18 rooms
What is the total number of rooms in the hotel?

Answers

Answer:

792

Step-by-step explanation:

Answer: 792 rooms



You just multiply 44 by 18!
Hope this helps!

Bill has 40 apples. Laurie has 8 times as
many apples.

Answers

If Laurie had 8 times as many apples as Bill's 40 apples, the equation would be 40 x 8. 40 x 8 = 320 :)

Answer:

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Step-by-step explanation:

In a bowl that has 12 jolly ranchers candies, there are 3 Yellow 5 Red and 4 Green. you pick two of these Jolly Ranchers from the bowl WITHOUT REPLACEMENT.
1 find the probability that both candies are red?

Answers

Answer:

0.15 or 20/132 or 5/33 or 15%

Step-by-step explanation:

5/12 is the probability for the first red candy.

The question says "without replacement" meaning that if one candy is picked it will NOT be picked again and it will not go back to the original bowl. The second red candy is 4/11 (one red candy was already taken out from the first event). Multiply 5/12 and 4/11 to get 20/132. That is simplified to be 5/33 but if you divide it will 0.15 and as a percent it would be 15%.

andrea needs a new air conditioning system

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Answer:

She should buy one that accords to her budget and her needs

PLEASE SOLVE AND EXPLAIN !!!

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Answer:

3.46

Step-by-step explanation:

A regular hexagon is shown below. Find the value of x.
(11x + 21)°

Answers

Answer:

x=9

Step-by-step explanation:

The expression is for the interior angle of the hexagon; one interior angle is equal to .

Since an interior angle of a hexagon measures 120°, we have the equality

.

Now it is just a matter of solving for  

11x=120-21

11x=99

x=99/11

x=9

The value of {x} for the hexagon shown is 9.

What is Hexagon?

A hexagon is a polygon with 6 equal sides. The perimeter of a hexagon is the sum of all the six lengths. The measure of the interior angle of a hexagon is 120 degrees.

Given is to find the value of {x} in the Hexagon shown below.

The measure of the internal angle of a hexagon is 120 degrees. So, we can write -

(11x + 21) = 120

11x = 120 - 21

11x = 99

x = 9

Therefore, the value of {x} for the hexagon shown is 9.

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The graph represents a quadratic function. Write the function in vertex form.

Answers

Answer:

y=3(x+3)^2-8

Step-by-step explanation:

Vertex form:

y=a(x-h)^2+k

h=-3, k=-8

y=a(x+3)^2-8

sub (-4,-5)

-5=a(-4+3)^2-8

a=3

y=3(x+3)^2-8

Mr.Rivera can grade 8 math tests in 10 minutes what is the teachers unit rate?

Answers

Answer:

0.8

Step-by-step explanation:

Answer: 1 minute and 25 seconds

Step-by-step explanation:

How many solutions does 5x+24=5(x+5)

Answers

Answer:

There are no solutions.

Please help me with this! I need this ASAP! Please help!

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Answer:

The 2nd and 3rd boxes are right, that is :-

* 2b is a term

and

* 9 is a constant

Fred bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Fred start with ?

Helpp I need this todayyyyyy

Answers

Answer:

86 - 9 = 77

Step-by-step explanation:

Look at the picture please!!!!

Answers

Answer for 1:

8x + 10

Answer for 2:

2x + 1

Answer for 3:

-3x - 15

Answer for 4:

2x + 10

Answer for 5:

-3x - 5

Answer for 6:

-17x - 3

Answer for 7:

8x - 18

Answer for 8:

-x + 4

Answer for 9:

4.8x + 5.6

Answer for 10:

1.25x + 1

Answer for 11:

The Dolphins won 7x + 10 more points than the Jaguars

Answer for 12:

The sandwich costs x + 1.01 more than the drink

Answer for 13:

Tuition costs 7x + 25 more than fees

Tuition costs 7x + 72 more than rooms and board

Answer:

1. 9x squared + 34x +21

2. 2x + 1

3. -3x + 15

4. 2x + 10

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6. -17x - 3

7. 8x- 18

8. -x + 4

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I think these are the correct answers. Sorry if I'm wrong. I hope this helped!

Step-by-step explanation:

Brainliest if correct Multiply 3/7 by 4/5

Answers

Answer:

Step-by-step explanation:

x1 / y1    times x2 / y2       where are two fractions

x1/y1 times x2/y2   = x1 times x2 / y1 times y2   = z1 / z2    z is a new fraction

fractions multiply like regular wholes number, which can also be represented in fractional form

Examples:

2/1   times 3/1 = 2x3 /1x1   6/1

10/2 x 18/3 = 180/6     now look at 10/2 = 5     18/3 = 6    5x6 =  30    

  5  x    6    = 30

Now apply to your fractions:

3/7 x 4/5   =   3x4 / 7x5    

12/35  

Select the correct answer.What is 2/5 divided by 4/7 by equal to?A.7/5 B.7/10 C.10/7 D.7/5

Answers

the answer would be A . 7/5

Answer:

5/7

Step-by-step explanation:

5/7

It is always good to double-check your math to make sure you did it right. When I entered 4/7 for x in this equation x / (4/5) = (5/7), we get the following true equation which means the math is correct.

(4/7) / (4/5) = (5/7)

When a certain basketball player takes his first shot in a game he succeeds with prob. 1/3. If he misses his first shot, he loses confidence and his second shot will go with prob. 1/4. If he misses his first 2 shots, his third shot will go with pro. 1/5. If he misses his first 3 shots, his fourth shot will go with prob. 1/6. If he misses his first 4 shots, the coach will remove hom from the game. Assume that the player keeps shooting until he succeeds or he is removed from the game. Let X denote the number of shots he misses until his first success or until he is removed from the game.

Required:
a. Compute the p.m.f. of X
b. Compute E[X]

Answers

Answer:

X : ____ 0 ____1 ____ 2 ____ 3 ____ 4

P(x) : _ 0.333_0.167 _0.100_0.067__0.333

E(X) = 1.9

Step-by-step explanation:

From the question above:

X ; number of misses

For :

X = 0 ; P(X = 0) = 1/3 = 0.333

X = 1 ; misses first ; succeeds on second

P(X = 1) = 2/3 * 1/4 = 2/12 = 1/6 = 0.167

X = 2 ; misses first, misses second, succeeds on third

P(X = 2) = 2/3 * (1 - 1/4) * 1/5 = 2/3*3/4*1/5 = 6/60 = 1/10 = 0.10

X = 3 :misses first, misses second, misses third succeeds on fourth

P(X = 3) = 2/3 * 3/4 * (1 - 1/5) * 1/6 = 2/3*3/4*4/5*1/6 = 24/360 = 0.067

X= 4

P(X =4) = 2/3 * 3/4 * 4/5 * 5/6 = 120/ 360 = 1/3 = 0.333

X : ____ 0 ____1 ____ 2 ____ 3 ____ 4

P(x) : _ 0.333_0.167 _0.100_0.067__0.333

E(X) :

Σx*p(x) = (0*0.333) + (1*0.167) + (2*0.100) + (3*0.067) + (4*0.333)

0 + 0.167 + 0.2 + 0.201 + 1.332

= 1.9

how many solutions does the system of equations have y-5x=-6 and 3y-15=-12​

Answers

Answer:

one solution

Step-by-step explanation:

to understand thisyou need to know about:system of linear equationPEMDAStips and formulas:a system of linear equation has only one solution if [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]let's solve:

define a,b

[tex]a_1=1[/tex][tex]a_2=3[/tex][tex]b_1=-5[/tex][tex]b_2=-15[/tex][tex] \sf substitute \: the \: value \: of \: a_1\: a_2 \: b_{1}\: b_{2} : \\ \sf \frac{1}{3} \neq \frac{ - 5}{ - 15} \\ \sf \frac{1}{ 3} \neq - \frac{1}{3} [/tex]

therefore

the system of linear equation has only one solution

What Is the dependent variable the shoe size or the height

Answers

Answer:

The dependent variable is the shoe size

Step-by-step explanation:

Determine the intercepts of the line.
y + 5 = 2(x + 1)
y-intercept:
T-intercept:

Answers

Answer:

3 5 minus 2 equal 3 plus 1 equals 4

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Answer: 1) y= 9, 4, 1, 0, 1, 4, 9

Step-by-step explanation:

Which graph represents the solution to (x – 3)2 + (y + 4)2 > 36?

Answers

Answer:

second choice

Step-by-step explanation:

edge

The region outside the circle is under the consideration. Then the correct option is B.

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x – h)² + (y – k)² = r²

The inequality equation of the graph is given below.

(x – 3)² + (y + 4)² > 36

(x – 3)² + (y + 4)² > 6²

From the equation, the radius of the circle will be 6 units and the center of the circle will be (3, –4).

The region outside the circle is under the consideration.

Then the correct option is B.

The graph is given below.

Learn more about the equation of a circle here:

https://brainly.com/question/10165274

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HELP PLEASE
68 POINTS!
BRAINLIEST

You can zoom in on the photo for it to be clearer!!

Answers

Hold up I’ll help u

What is 5/9 divided by 4/9 answer

Answers

Answer:

1.25

Step-by-step explanation:

5/9 divided by 4/9 is 1.25

Pls help .............................

Answers

Pythagorean theorem you times 40 by 2 then 9 by 2 then square root

If f(x) = x* and g(x) = 3+8x?, find g(f(x)).

Answers

g(8x-3)=x

have a good day

For the function f(x) = -3sin(x) + 2, the distance between the maximum and minimum values is 6. Which statement must be true about this function? HINT: It's not B.

A. The amplitude is 3.
B. The midline is y = 3.
C. The period of the function is 3pi.
D. The range is [-3, 3].

Answers

Answer: A. The amplitude is 3.

Step-by-step explanation:

Given function : [tex]f(x) = -3sin(x) + 2[/tex]

Period of a sine function is [tex]2\pi.[/tex]

Since [tex]-1\leq \sin x \leq 1[/tex]

[tex]\Rightarrow\ -3\leq -3\sin x\leq 3\\\\\Rightarrow\ -3+2\leq -3\sin x+2\leq 3+2\\\\\Rightarrow\ -1\leq -3\sin x+2\leq 5[/tex]

i.e. Range is [-1,5]

Amplitude = 3 [coefficient of sin x]

Only option A. is correct.

f(2)=−14 and g(2)=13 Find (f+g)(2).

Answers

Answer: The value of (f+g)(2) = -1

Step-by-step explanation:

Given: f(2)=-14 and g(2)=13

To find: (f+g)(2)

Addition of two functions:

(f+g)(x) = f(x)+g(x)

Then, (f+g)(2) = f(2)+g(2)

(f+g)(2)  = -14+13  [given]

(f+g)(2)  = -1

Therefore , the value of (f+g)(2) = -1

Suppose a tree limb falls on your house during a storm and causes $9,500 worth of damage to your pool cage. The premium for your homeowners insurance is $150/month, and your deductible is $4,000 with an out-of-pocket maximum of $10,000. If this event is a covered event, how much will you need to pay a contractor to repair the damage to the pool cage?

A: $4000
B: $9500
C$10,000

Answers

Answer:B

Step-by-step explanation:

The amount you need to pay a contractor to repair the damage to the pool cage should be considered as the option b $9,500

Calculation of the amount:

Since the amount of $9,500 should be considered as the worth of damage to your pool cage.

Also there are other charges like premium, deductible amount, pocket maximum amount, etc.

So based on the payment only $9,500 should be conisdered.

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Match each equation with the appropriate type of factoring.

1.
12x2−44x+7
2.
18x3−2x2+27x−3
3.
x2+5x−36
4.
4x2−81
5.
32x3−4

Difference of Squares


GCF


Grouping


Quadratic Trinomial a≠1


Quadratic Trinomial a=1

Answers

I’m not sure what the answer is but I hope someone can help you

Anyone know? Thanks

Answers

Answer:

the answer is the x-intercepts are about(0,-6) and (0,2) hope this helps

Step-by-step explanation:

Find the area of the shape shown below.

Answers

Answer:

10 square units.

Step-by-step explanation:

Remark

No matter how weird it looks, the figure is a trapezoid. It has 2 parallel lines.

The height has 2 right angles, one at each end.

Givens

b1 = 2

b2 = 8

h = 2

Formula

Area = 1/2 * (b1 + b2 ) * h

Solution

Area = 1/2 * (2 + 4 + 2 + 2) * 2    Be sure you understand where all those 2s came from.

Area = 10 square units

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