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
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.
PLEASE HELPPPPPPPP !!!!!!!!!!!!!!1
Answer:
-8.45, 0.95, 8.25
Step-by-step explanation:
The easiest way to do this is to convert the fraction to a decimal, and then compare the values.
8 8/32 is equal to 8 and 1/4. Because 1/4 = 0.25, 8 and 8/32 equals 8.25.
Now, let's compare values.
Numbers we need to compare: -8.45, 0.95, 8.25
The smallest number is -8.45, then 0.95, and lastly, 8.25.
Thus the answer is
-8.45, 0.95, 8.25
NEED ASAP BEFORE MARCH 11
PLS HELP.I WILL MARK BRAINLIEST!!
Answer:
Answer in attachment photo
Sumi earns $6.30 in 1/2 hr at her job at the Pet food store. If she works for 60 hours how much will she make in total?
Answer:
$756.00
Step-by-step explanation:
6.30 x 2 = 12.60/hour
12.60 x 60 = $756.00
so 29 is a monomial also
Answer:
yes, 29 is a monomial
Step-by-step explanation:
HELP PLZ 3MINS ITS DUEE
Answer:
11
Step-by-step explanation:
1/2 times 2³=4
+7=11
(30)Points
Which Statement is true
A,
B.
C.
D.
Answer:
The first answer one is true
help me and thank you
Answer:
15.736
Step-by-step explanation:
7 in.
5 in.
7 in.
5 in.
The perimeter?
Answer:
The perimeter is:
24
Step-by-step explanation:
Perimeter is the outside frame of the area. Add the dimensions together to get your answer. Adding:
7+7= 14
5+5= 10
10+14= 24
:) Hope this helps have a wonderful day!
Maria claims that ΔABE ≅ ΔACD .
Select two of the transformations or series of transformations that support Maria's claim and maps ΔABE to ΔACD.
A dilation with a scale factor of 3 about point A.
A dilation with a scale factor of 2 about point B.
A dilation with a scale factor of 2 about point A followed by a translation of 4 units downward.
A dilation with a scale factor of 3 about point B followed by a translation of 4 units downward.
A dilation with a scale factor of 3 about point A followed by a translation of 8 units to the right.
A dilation with a scale factor of 2 about point B followed by a translation of 8 units to the right.
Answer:
Two transformations or series of transformation that support Maria's claim and Maps ΔABE to ΔACD are;
A dilation with a scale factor of 3 about point A
A dilation with a scale factor of 3 about point B followed by a translation of 4 units downwards
Step-by-step explanation:
Using an online source, we have;
ΔABE ~ ΔACD
The coordinate of triangle ΔABC are;
A(-6, 4), B(-6, 2), and E(-2, 2)
The coordinate of triangle ΔACD are;
A(-6, 4), C(-6, -2), and D(6, -2)
∠A ≅ ∠A by reflexive property
Segment BE ║Segment CD and segment DE and segment AE are collinear on transversal AD
∴ ∠E ≅ ∠D Corresponding angles
∴ ΔABE ~ ΔACD by Angle-Angle rule of congruency
Segment AB on ΔABE and segment AC on triangle ΔACD are corresponding sides on both triangles
The length of segment AB on ΔABE = 2 units
The length of segment AC on ΔACD = 6 units
The scale factor of dilation, SF = (The length of segment AC)/(The length of segment AB)
∴ SF = (6 units)/(2 units) = 3
Therefore, ΔABE maps to ΔACD by either of the following;
1) A dilation with a scale factor of 3 about point A
2) A dilation with a scale factor of 3 about point B followed by a translation of 4 units downwards.
Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you Created? PLEASE PUT IT INTO LITTLE WORDS IM ONLY IN MIDDLE SCHOOL
NO PLAGIARISM
Answer:
Explained below.
Step-by-step explanation:
There are quite a few examples of this but I will go with what is common in physics which is "acceleration due to gravity".
Acceleration due to gravity is positive when an object is falling down in the direction of gravity but negative when it is thrown upwards and acting against gravity motion.
Thus;
g_downwards = 9.8 m/s²
g_upwards = -9.8 m/s²
If acceleration due to gravity is zero, it means that the object is at the centre of the earth because at that point g = 0.
Answer:
A miner digs 100ft underground. Then he went up to the surface and climbed all the way to the top of the mountain. The entrance of the underground cave represents 0.
Step-by-step explanation:
Question 3 (5 points)
(02.01 MC)
Which of these is a positive externality of carpooling with friends to work?
оа
Reduced commute time
Ob
Reduced driving focus
Ос
Reduced traffic on the road
Od
Reduced time to socialize
Answer:
reduced traffic on the road
Step-by-step explanation:
just took the test :)
Answer: C) Reduced traffic on the road
Step-by-step explanation: Ive taken this test
868 ÷ 14 = ?? i need help lol
Answer:
**********************868/14=62********************
Step-by-step explanation:
Answer:
+*~868 ÷ 14 = 62~*+
(Hope this helps! Btw, I answered first. Brainliest please! :D)
In AMNO, the measure of O=90°, the measure of N=31°, and OM = 11 feet. Find
the length of MN to the nearest tenth of a foot.
Answer:
21.4
Step-by-step explanation:
just trust me i come from DeltaMAth
What is the probability of getting a vowel if you randomly pick a letter from the English alphabet?
Find the equation of the line
Use exact numbers
I thank you very very much in advance!
Answer:
y = 3/4x -2
Step-by-step explanation:
Points on the graph: (4, 1) and (0, -2)
Slope:
m=(y2-y1)/(x2-x1)
m= (-2-1)/0-4)
m=(-3)/(-4)
m = 3/4
Point-slope:
y - y1 = m(x - x1)
y - 1 = 3/4(x - 4)
y - 1 = 3/4x - 3
y = 3/4x -2
Maya obtains a $423,000 30/10 balloon mortgage with a rate of 5.65%. What will her monthly payments be? (2 points)
Answer:
Her monthly payment is approximately $4,611.65
Step-by-step explanation:
The monthly payment on the loan is given by the following formula;
[tex]A = P \cdot \dfrac{r\cdot (1 + r)^n}{(1 + r)^n - 1}[/tex]
A = The monthly payment
P = The principal amount = $423,000
r = 5.65%
The number of years = 10 years
[tex]A = 423,000 \cdot \dfrac{\dfrac{0.0565}{12} \cdot \left (1 + \dfrac{0.0565}{12} \right )^{180}}{\left (1 + \dfrac{0.0565}{12} \right )^{180} - 1} \approx 4611.65[/tex]
Her monthly payment, A ≈ $4,611.65
Which property of addition is shown?
-3 + 5 = 5 + (-3)
HELPPOPP PLEASEEE!!!!!!!!!!!!
Answer:
$ 100 is saved by paying the total amount at the time of purchase
Step-by-step explanation:
its Originally 800 but You put down 200 leaving it At 600 But 50 time 10 is 500 plus 200 more Because you pay 200 more for the last 4 months So 500 plus 200 is 700 plus the 200 you put down And it would be 900 instead of 800
What is the area of the rectangle above?
A.
84 square units
B.
19 square units
C.
38 square units
D.
78 square units
Solve this system of equations using the
elimination method.
Answer:
4x-3y=-10 ans C
2x+3y=4
Step-by-step explanation:
4x-3y=-10--------eqn 1
2x+3y=4----------eqn 2
multiply eqn 1 by 2 and eqn 2 by 4
8x-6y=-20
8x+12y=16
subtract eqn 2 from 1
8x-8x ,12-(-6y)=16-(-20)
18y=36
divide both sides by 18
y=2
substitute y=2 in eqn 1
4x-3(2)=-10
4x-6=-10
4x=-10 + 6
4x= -4
divide both sides by 4
x= -1
There just help bsf Kelly
Round to the nearest hundredth 94.855
Pls help me on this due in 10 mins
Answer:
A, E, G
Step-by-step explanation:
Answer:
A
E
G
Step-by-step explanation:
When you divide A, E, and G with the common factor, they all equal 5 : 9
What is the average weight of the kittens in the shelter?
Please explain!!
Answer:
Step-by-step explanation:
You should add the weights of each kitten and then divide by the number of kittens. Ex. There are 5 kittens weighing 2, 1, 3, 2, and 2. So you would add those to get 10 and divide by the number of kittens which is 5 to get an average of 2.
So in this case you would first add the weight of the kittens
Then divide that by the number of kittens
Then the quotient would be the average of the weight of the kittens in the shelter.
Choose the function whose graph is a parabola.
O y=x+91
O y=3
O y=x2-10
O y=-2x
Answer:
O y=x^2-10
Step-by-step explanation:
x^2 = parabola
the rest are just linear equations
One-half a number minus 6 is 4
Answer:
the answer is 20
20/2 = 10
10- 6 =4
Elly's hot dog emporium is famous for its chili dogs. Some customers order the hot dogs with hot peppers, while many do not care for that added bit of zest. Elly's latest sales indicate that 30% of the customers ordering her chili dogs order it with hot peppers. Suppose 18 customers are selected at random. What is the probability that between two and six people inclusive want hot peppers?
Answer:
here you go
Step-by-step explanation:
2 1/4 as a single fraction
Answer:
9/4
Step-by-step explanation:
Answer:
9/4
Step-by-step explanation: