Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. a bank conducts interviews of job applicants with the use of the lie detector. there are 15 applicants who are interviewed.
a.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that all 15 are telling the truth?
b.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that at least one is lying?
c.what are the mean and standard deviation of the 15 applicants the lie detector concludes are lying?
d.what is the probability that the number of truthful applicants classified as liars is greater than the mean?

Answers

Answer 1

Part A:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector correctly determined that a selected person is saying the truth has a probability of 0.85
Thus p = 0.85

Thus, the probability that the lie detector will conclude that all 15 are telling the truth if all 15 applicants tell the truth is given by:

[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(15)={ ^{15}C_{15}(0.85)^{15}(0.15)^0} \\ \\ =1\times0.0874\times1=0.0874[/tex]

Part B:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.25
Thus p = 0.15

Thus, the probability that the lie detector will conclude that at least 1 is lying if all 15 applicants tell the truth is given by:

[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(X\geq1)=1-P(0) \\ \\ =1-{ ^{15}C_0(0.15)^0(0.85)^{15}} \\ \\ =1-1\times1\times0.0874=1-0.0874 \\ \\ =0.9126[/tex]

Part C:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The mean is given by:

[tex]\mu=npq \\ \\ =15\times0.15\times0.85 \\ \\ =1.9125[/tex]

Part D:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The probability that the number of truthful applicants classified as liars is greater than the mean is given by:

[tex]P(X\ \textgreater \ \mu)=P(X\ \textgreater \ 1.9125) \\ \\ 1-[P(0)+P(1)][/tex]

[tex]P(1)={ ^{15}C_1(0.15)^1(0.85)^{14}} \\ \\ =15\times0.15\times0.1028=0.2312[/tex]

Related Questions

the cost of internet access at a cafe is a function of time the cost for 8, 25, and 40 minutes are shown write the equation in slope-intercept form that represents the function then find the cost of surfing the web at the cafe for one hour

Answers

Answer:

Step-by-step explanation:

Where is the graph?

Jamie has applied for a credit card. The APR of the card is 20%. What will be the monthly interest rate?

Answers

apr means annual percentage rate and there are 12 months in a year so:

20/12 = 1.67%

Answer:

1.67%

Step-by-step explanation:

The APR of a card is the Annual Percentage Rate. This is the yearly rate of interest that a person has to pay on the money he or she borrowed. Interest is a price that is paid for borrowing money. In this case, if the APR is 20%, we would need to divide this number by the number of months in a year in order to get the monthly interest rate:

20 / 12 = 1.67 %

What is the area of the figure?

Answers

see attached picture:

Which of the points listed is the same distance from the y-axis as the point (−1.5, 6)?

Answers

the complete question in the attached figure

we know that
the distance from a point to line (y-axis) is the perpendicular line against y-axis, which is the absolute value of x-coordinates

in this problem
the point (−1.5, 6)
the absolute value of x-coordinates is 1.5
hence
the distance is 1.5

therefore

the answer is
the option B) the point (1.5,-3)

One aluminum can weights 1/25 pound. If your school starts a recycling drive how many cans will your school need to collect to recycle one ton?

Answers

Hello!

First you have to find how many cans make a pound

1/25 * 25 = 1

It takes 25 cans to get to 1 pound

There are 2000 pounds in a ton

Multiply the amount of cans to make a pound by the amount of pounds in a ton

25 * 2000 = 50000

The answer is 50,000 aluminum cans

Hope this helps!

Which of the following is the prime factored form of the lowest common denominator of?
A.2 x 2 x 2 x 3
B.2 x 4 x 2 x 3
C.8 x 6
D.2 x 12

Answers

A is the prime factored form of the lowest common denominator

2 x 2 x 2 x 3 factored form is the prime factored form.

What is a prime number?

"A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers."

The given factored forms are:

A. 2 x 2 x 2 x 3

Here, all the numbers are prime numbers.

Therefore, this factored form is the prime factored form.

B. 2 x 4 x 2 x 3

Here, all the numbers are not prime numbers.

Therefore, this factored form is not the prime factored form.

C. 8 x 6

Here, not a single number is prime number.

Therefore, this factored form is not the prime factored form.

D. 2 x 12

Here, all the numbers are not prime numbers.

Therefore, this factored form is not the prime factored form.

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What is the letter ƒ in mathematics?

Answers

The letter f usually indicates that the equation is a function in the notation f(x).

Example: f(x) = x + 1

It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).

OR

It could just be a regular ole variable

Example: f + 1 = 7, solve for f

The letter f usually indicates that the equation is a function in the notation f(x).

Example: f(x) = x + 1

It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x).

It could just be a regular ole variable

Example: f + 1 = 7, solve for f

please help me answer these!!!

Answers

You don't have to look very far in either case. Both answers are "a".

1. Checking selection "a",
265 =? 35 +20*7 = 35 +140 = 175
a (7, 265) is NOT a solution

2. Checking selection "a",
18 =? 5*4 -2 = 20 -2 = 18
a (4, 18) IS a solution

jose bought 8 bags of oranges.each bag weighed 12 ounces. there are 16 ounces in a pound.how many pounds of oranges did jose buy

Answers

Hello!

First you have to find the amount of ounces the oranges weigh

To find this you multiply the amount of oranges by the how much they weigh

12 * 8 = 96

Divide this by the amount of ounces is in a pound

96 / 16 = 6

The answer is 6 pounds

Hope this helps!

5-2i and 7+6i find the midpoint

Answers

That would be (5, -2) and (7, 6) on complex plane. You can use midpoint formula

So that would be ((5+7) / 2, (-2+6) / 2) = (6, 2)

So then answer would be 6+2i

Final answer:

The midpoint between the complex numbers 5-2i and 7+6i is 6 + 2i.

Explanation:

To find the midpoint between two complex numbers, we can use the formula:

Midpoint = (Re(z1) + Re(z2))/2 + (Im(z1) + Im(z2))/2i

Applying the formula to the given complex numbers 5-2i and 7+6i, we have:

Midpoint = (5 + 7)/2 + (-2 + 6)/2i
Midpoint = 12/2 + 4/2i
Midpoint = 6 + 2i

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A test has forty questions worth 100 points.The test consists of True/False questions worth 3 points each and multiple choice questions worth 2 points each. How many multiple choice questions are on the test?

Answers

20 multiple choice questions

Answer:

20 multiple choice questions

Step-by-step explanation:

I hope this help you out

A video posted on the internet is becoming very popular,and the total number of views is increasing by 40% every hour if the video currently has 38,000 views how many views will it have in 2 hours

Answers

Final answer:

The video with an initial 38,000 views will have approximately 74,480 views in 2 hours when it is increasing by 40% every hour.

Explanation:

To calculate the number of views a video will have in 2 hours if it is increasing by 40% every hour, we will use the formula for percentage growth. Initially, the video has 38,000 views. After one hour, the views will be increased by 40%, and after two hours, this new amount will again be increased by 40%. The formula for calculating the number of views after each hour is:

Views after n hours = Initial views × [tex](1 + growth rate)^n[/tex]

Where:

Initial views = 38,000

Growth rate = 40% = 0.40 (as a decimal)

n = number of hours

After 1 hour:

Views after 1 hour = 38,000 × (1 + 0.40)^1

Views after 1 hour = 38,000 × 1.40 = 53,200

After the second hour, we will use the number of views from the first hour to calculate the increase:

Views after 2 hours = 53,200 × [tex](1 + 0.40)^1[/tex]

Views after 2 hours = 53,200 × 1.40 = 74,480

Therefore, the video will have approximately 74,480 views in 2 hours.

hey can you please help me posted picture of question

Answers

Answer:
f⁻¹(x) = [tex] \frac{x+6}{7} [/tex]

Explanation:
To get the inverse of a function, we will follow these steps:
1- replace f(x) with y
2- swap the x and y variables
3- solve for y
replace y with f⁻¹(x)

Applying this to the given as follows:
f(x) = 7x - 6

Step 1: replace f(x) with y:
y = 7x - 6

Step 2: swap the x and y variables:
x = 7y - 6

Step 3: solve for y:
7y = x + 6
y = [tex] \frac{x+6}{7} [/tex]

Step 4: replace y with f⁻¹(x):
f⁻¹(x) = [tex] \frac{x+6}{7} [/tex]

Hope this helps :)

For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.

Answers

V = 4/3 (pi r times ^3) = formula for this knowing that you than

Combine volumes up (1ft times 3.14) + (2ft times 3.14) + (3ft times 3.14)

18.8 >. rounded to the nearest cubic foot of 19

What is the value of y?

11.6 ft
12.5 ft
16.5 ft
17.5 ft

Answers

we know that

in the triangle BCD
cos C=8/14
C=arc cos (8/14)-----> C=55.15°

sin C=BD/14---------> BD=14*sin 55.15------> BD=11.49 ft

in the triangle ABC
180=∡A+∡B+∡C
∡A=180-(90+55.15)-----> ∡A=34.85°

tan A=BD/y-------> y=BD/tan A-----> y=11.49/tan 34.85----> y=16.50 ft

the answer is
y=16.50 ft

To solve the exercise shown in the picture attached, you must apply the following proccedure:

1. First, you must apply the Pythagorean Theorem to calculate the heigth of the triangle, as below:

a^2=b^2+c^2
b=√(a^2-c^2)
b=√(14)^2-(8)^2
b=√132
b=11.48

2. Now, you must calculate the angle ∠BC, as below:

Sin(α)^-1=opposite/hypotenuse
Sin(BC)^-1=8/14
∠BC=34.84°

3. Therefore, the angle ∠BA is:
∠BA=90°-34.84°
∠BA=55.15°

4. Then, you have:

Tan(55.15°)=y/11.48
y=16.48

it took a ball 1 minute to roll 90 feet. what was ths balls average rate of speed in feet per second

Answers

1.5 ft per second.

Divide the 90 by 60.

a band that will be the opening act for a concert charges a $700.00 flat fee as well as 16% of all ticket profits from ticket sales. if the band earned $1,200, how much was made in total ticket sales for the show?

Answers

The band earned $1,200.

1. Subtract the flat fee 1,200-700 =500
2. 500 is what just the band made. Divide that by .16 (16%) to get the total ticket amount... 500 divided by .16 = 3,125

The total ticket amount was $3,125.

Ben runs around the track at a pace of 1 lap every 80 seconds. Sally runs on the track in the opposite direction. The two meet every 30 seconds. How long does it take Sally to run each lap around the track?

Answers

48 seconds, Consider what happens between one time that Ben and Sally meet and the next. During this period Ben runs 30 (seconds)/80 (seconds/lap) = 3/8 of a lap. So Sally runs 5/8 lap in the same time. Her speed is therefore 5/8 (laps)/ 30(seconds) which amounts to 1 (lap)/ 48 (seconds).

The current size of an image on Samuel's computer is shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 8 inches and the width is labeled as width equal to 10 inches. What are the dimensions of the image at fraction 1 over 2 times its current size

Answers

Length is equal to 4 and width is equal to 5.

You can just divide each by 2.

Answer:

The length and the width of image is 4 inches and 5 inches respectively

Step-by-step explanation:

Given : Length of rectangle is 8 inches

Width of rectangle is 10 inches

To Find: What are the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size

Solution:

Length of rectangle is 8 inches

Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size

So, Length of image = [tex]\frac{1}{2} \times 8 = 4[/tex]

Thus the length of image is 4 inches.

Width of rectangle is 10 inches

Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size

So, width of image = [tex]\frac{1}{2} \times 10 = 5[/tex]

Thus the width of image is 5 inches.

Hence the length and the width of image is 4 inches and 5 inches respectively.

Find the measure of the missing angle of a triangle, if two of its angles are 75 degree and 65 degree respectively. please show work

Answers

The sum of the angles in a triangle is 180°. That is ...
75° +65° +(missing angle) = 180°
(missing angle) = 180° -75° -65°
(missing angle) = 40°

A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. a piece of plastic on the front rim makes a clicking sound every time it passes through the fork. if the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she traveled? (a) 0.50 km (b) 1.5 km (c) 1.0 km (d) 0.80 km (e) 1.8 km

Answers

we know that
circumference=2*pi*r
for r=0.50 m
circumference=2*pi*0.50-----> pi m

1 click correspond to a length of--------> pi meter
320 click---------------> x
x=320*pi-----> x=1005.31 meters-------> 1 km

the answer is
the option (c) 1.0 km

How would the expression x^3+8 be written using Sum of Cubes?

Answers

Given expression is:

x³ + 8

8 is the cube of 2, so we can write the above expression as sum of two cubes as:

x³ + 2³

Using the formula of sum of cubes, we can write:

x³ + 2³ = (x + 2)(x² - 2x + 4)

Thus, option B gives the correct answer

plz help ill give u brainlist plz some one help fast it is esy in just dume

Answers

There are 70 questions. The probability of getting any one of the questions right is 0.2. That's because there are five answers only one of which is correct.

If there are 5 questions and you want to pick the right one the probability is 1/5. If you don't know how to find that, let your calculator walk you to the answer.

1
÷
5
=
And it will tell you that it is 0.2.

So if you blindly (not brainly) fill in the multiple choice answer sheet, the number you will get right is
(P(0.2) * The total number of questions or
0.2 * 70 = 14
Just pure dumb luck will give you 14 correct answers.

hello can you please help me posted picture of question

Answers

Total number of numerals = 10
Total number of numerals to be used = 6
We are to find the number of different codes that can be formed and those can be found by permutations.

We have to find the permutations of 10 numerals taken 6 at a time. So we are to find 10P6.

10P6 = 151200

So, 151200 different codes can be formed.

So the answer to this question is option A

Looking at the ping-pong ball toss board below, whats the probability of landing on a gray square? (Note the board contains 5 rows of 5 squares.)

Answers

the probability of landing on a gray square = 5/25 = 1/5

answer
D. 1/5

Answer:

Option D. [tex]\frac{1}{5}[/tex] is the correct option.

Step-by-step explanation:

Total number of solution sets n(S) (sample space) = 5×5 = 25

(Since a ping-pong ball can land on any block of the toss board so total number of events which can occur will be = 25)

Now preferred events n(E) = 5

(Since number of grey squares where ping-pong ball can land are = 5)

Therefore probability of landing of ping pong ball on a grey square P(E) = [tex]\frac{n(E)}{n(S)}[/tex]

P(E) = [tex]\frac{5}{25}[/tex]

P(E) = [tex]\frac{1}{5}[/tex]

Therefore, Option D. [tex]\frac{1}{5}[/tex] will be the answer.

which best describes the meaning of the term theroem?

Answers

The wording of your question implies that there are answer choices to choose from. I would reupload with an attachment of the answer choices for the most accurate response. If not, here's a picture of the definition of a "theorem."

Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:

Answers

Price elasticity is defined as [tex]\frac{\Delta(quantity)}{\Delta(price)}[/tex].

Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0

We calculate
[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)

Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)

The required value of elasticity at x = 65 is -0.007.

Given that,

The demand equation for a certain item is [tex]1p + 1x^{2} -160 = 0[/tex].

We have to determine,

The value of elasticity at 65.

According to the question,

The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.

Therefore,

Price of elasticity = [tex]\frac{dp}{dx}[/tex]

Calculate change by differentiation with respect to p:

[tex]\dfrac{d(p+x^{2} -160)}{dx}\\\\1 + 2x\frac{dp}{dx} = 0\\[/tex]

Then,

[tex]E(x) = \frac{dp}{dx} = \frac{-1}{2x}[/tex]

Therefore, The elasticity at x = 65 is ,

[tex]E(65) = \frac{-1}{2(65)} = -0.007[/tex]

Hence, The required value of elasticity at x = 65 is -0.007.

For more information about Elasticity click the link given below.

https://brainly.com/question/14547451

Question 11 Unsaved
Find the domain, period, range, and amplitude of the cosine function.

y = -6cos4x

Answers

For this case we have the following function:
y = -6cos4x
The function is defined for all values of x, therefore, the domain is:
(-inf, inf)
The range of the function is:
For x = 0
y = -6cos (4 (0))
y = -6cos (0)
y = -6 (1)
y = -6
For x = pi / 4
y = -6cos (4 (pi / 4))
y = -6cos (pi)
y = -6 (-1)
y = 6
The range of the function is:
[-6, 6]
The amplitude of the function is:
6
Answer:
Domain: (-inf, inf)
Range: [-6, 6]
Amplitude: 6

which transformations are needed to change the parent some function to the sine function below?

Answers

Beginning with the function y = sin x, which would have range from -1 to 1 and period of 2pi:
Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.

The first choice is the answer:
Solution:the function y = sin x, which would have range from -1 to 1 and period of 2pi:
So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2

Q10 Q2.) Find the standard form of the equation of the parabola satisfying the given conditions.

Answers

To solve this problem you must apply the proccedure shown below:

1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:

Focus: (-1,4) and Directrix: y=2

2. Therefore you have:

√(x0-(-1))²+(y0-4)²=|y0-2|
(x0+1)²+(y0-4)²=(y0-2)²

3. When you simplify the expression above and clear y0, you obtain:

y0=y

y=1/4(x²+2x+13)
y=(x²/4)+(x/2)+(13/4)

Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)

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