Help help , please help!! Giving brainliest if correct . The x-values in the table for f(x) were multiplied by -1 to create the table for g(x) What is the relationship between the graphs of the two functions? A. They are reflections of each other across the y-axis B. They are reflections of each other across the x-axis C. The graphs are not related D. They are reflections of each other over the line x = y

Answer:

2.16% probability that he would have done at least this well if he had no ESP

Step-by-step explanation:

For each coin toss, there are only two possible outcomes. Either he predicts the correct outcome, or he does not. The tosses are independent. So 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.

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

Coin is flipped 25 times

So [tex]n = 25[/tex]

What is the probability that he would have done at least this well if he had no ESP?

[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)[/tex]

In which

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

[tex]P(X = 18) = C_{25,18}.(0.5)^{18}.(0.5)^{7} = 0.0143[/tex]

[tex]P(X = 19) = C_{25,19}.(0.5)^{19}.(0.5)^{6} = 0.0053[/tex]

[tex]P(X = 20) = C_{25,20}.(0.5)^{20}.(0.5)^{5} = 0.0016[/tex]

[tex]P(X = 21) = C_{25,21}.(0.5)^{21}.(0.5)^{4} = 0.0004[/tex]

[tex]P(X = 22) = C_{25,22}.(0.5)^{22}.(0.5)^{3} = 0.0001[/tex]

The others(23, 24 and 25) are close to 0.

[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) = 0.0143 + 0.0053 + 0.0016 + 0.0004 = 0.0216[/tex]

2.16% probability that he would have done at least this well if he had no ESP

Answer:

[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]    

[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]    

The confidence interval is given by (49.94, 59.26)

Step-by-step explanation:

Info given

[tex]\bar X=54.6[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=9.2 represent the sample standard deviation

n=48 represent the sample size  

Part a

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=48-1=47[/tex]

The Confidence is 0.999 or 99.9%, and the significance is [tex]\alpha=0.001[/tex] and [tex]\alpha/2 =0.0005[/tex], and the critical value would be [tex]t_{\alpha/2}=3.51[/tex]

And replacing we got:

[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]    

[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]    

The confidence interval is given by (49.94, 59.26)

Answer:

The rule of reflection over y-axis is  (x,y)→(-x ,y)

M(-5,4) →M¹( 5 , 4)

N(-3,2) →N¹(3 ,2)

L(-6,2) →L¹( 6,2)

Step-by-step explanation:

Explanation:-

Type of transformation                     change to co-ordinate point

Reflection over x-axis                          (x,y)→(x ,-y)

Reflection over y-axis                          (x,y)→(-x ,y)

Given co-ordinate is M(-5,4)

The reflection over y-axis is  (x,y)→(-x ,y)

M(-5,4) →( 5 , 4)

N(-3,2) →(3 ,2)

L(-6,2) →( 6,2)

Answer: the answer is a

Step-by-step explanation:

Hope that helped

Answer:

11e+5f

Step-by-step explanation:

Combine like terms:

4e+7e+6f-f

11e+5f

Answer:

11e   +5f

Step-by-step explanation:

4e + 6f + 7e - f​

Combine like terms

4e+7e      +6f-f

11e   +5f

Answer:

3,325,140 Joules

Step-by-step explanation:

Work done by the pump = Force applied to pump * distance covered by the water.

Since Force = mass * acceleration due to gravity

Force = (density of water * volume of the tank) * acceleration due to gravity

F =ρVg

Workdone = (ρVg )* d

Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m

[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]

Workdone by the pump = 1000 * 113.10 * 9.8 * 3

Workdone by the pump  = 3,325,140Joules

Answer:

a. The number of light bulbs that burn out in the next year in a room with 19 bulbs: is a discrete random variable.

b. The usual mode of transportation of people in City Upper A: is not a random variable because its outcome isn't numerical.

c. The number of statistics students now doing their homework: is a discrete random variable.

d. The number of home runs in a baseball game: is a discrete random variable.

e. The exact time it takes to evaluate 67 plus 29: is a continuous random variable.

f. The height of a randomly selected person: is a continuous random variable.

Step-by-step explanation:

A random variable often used in statistics and probability, is a variable that has its possible values as numerical outcomes of a random experiment or phenomenon. It is usually denoted by a capital letter, such as X.

In statistics and probability, random variables are either continuous or discrete.

1. A continuous random variable is a variable that has its possible values as an infinite value, meaning it cannot be counted.

Example are the height of a randomly selected person, time it take to move from Texas to New York city, etc.

2. A discrete random variable is a variable that has its possible values as a finite value, meaning it can be counted.

Examples are the number of light bulbs that burn out in the next year in a room with 19 bulbs, the number of chicken in a district etc.

Answer:

A random variable in statistics can be loosely defined as a variable whose values depend on the outcome of a random phenomenon. These variables are variables that can be the results of an experiment not yet performed, or the results of an already performed experiment whose already existing result is uncertain.

A discrete random variable is finite and has a countable range of values.

A continuous random variable takes on numerical values in an interval of values and has no countable range of value.

a. The number of light bulbs that burn out in the next year in a room with 19 bulbs---   discrete random variable

b. The usual mode of transportation of people in City Upper A---  

not a random variable

c. The number of statistics students now doing their homework ---   discrete random variable

d. The number of home runs in a baseball game ---   discrete random variable

e. The exact time it takes to evaluate 67 plus 29 ---   continuous random variable

f. The height of a randomly selected person---   continuous random variable

Answer:

Step-by-step explanation:

Portuguese - Brazil

Estudam - A

Jogam - B

A=50

B=15

A∩B = 15

Somente estudam = 50 - 15 = 35

Somente jogam = 25

Nem estudam nem jogam = 5

Answer:

y = 1/-20 (x-2) - 5

Step-by-step explanation:

Focus = (a,b) = (2,-4)

So a = 2, b = -4

Directrix: y = -6

But y = k

So k = -6

Finding Standard Form of Equation for parabola

y = (1/2(b-k))(x-a)²+(1/2)(b+k)

y = (1/2(-4-6))(x-2)+(1/2)(-4-6)

y = (1/2(-10))(x-2)+(1/2)(-10)

y = (1/-20)(x-2)+(-5)

y = 1/-20 (x-2) - 5

Answer:

Down below

Step-by-step explanation:

The equation [tex]F(x) =(2)^x[/tex] can also be written as [tex]y=2^x[/tex] , because F of x of f(x) is actually y

Answer;

1) The t-distribution is most suitable for this problem.

2) Test statistic = 2.356

3) p-value = 0.0214

4) Alpha = 5% = 0.05

5) The p-value is greater than the significance level at which the test was performed, meaning that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.

Step-by-step Explanation:

Wife's score 2 2 3 3 4 2 1 1 2 4

Husband's score 2 1 2 3 2 1 1 1 2 4

To conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife, we first take the difference in the respomses of wives and husbands

x = (wife's score) - (husband's score)

Wife's score 2 2 3 3 4 2 1 1 2 4

Husband's score 2 1 2 3 2 1 1 1 2 4

Difference | 0 | 1 | 1 | 0 | 2 | 1 | 0 | 0 | 0 | 0

To use the hypothesis test method, we have to make sure that the distribution is a random sample of the population and it is normally distributed.

The question already cleared these two for us that this sample size is randomly selected from the population and each variable is independent from the other.

The question also already explained that the distribution is assumed to be normally distributed.

1) The distribution to use for this test is the t-distribution. This is because the sample size isn't very large and we have no information about the population mean and standard deviation.

For any hypothesis testing, we must first define the null and alternative hypothesis

Since we want to investigate whether the husbands are happier, that the mean difference is negative, that is less than 0,

The null hypothesis, which normally counters the claim to be investigated, would be that there isnt evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness isn't less than 0, that it is equal to or greater than 0.

And the alternative hypothesis, which usually confirms the claim to be tested, is that there is significant evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness is less than 0.

Mathematically, if μ is the mean difference in happiness of wives and husbands,

The null hypothesis is represented as

H₀: μ ≥ 0

The alternative hypothesis is represented as

Hₐ: μ < 0

2) To obtain the test statistic, we need the mean and standard deviation first.

Mean = (sum of variables)/(number of variables) = (5/10) = 0.5

Standard deviation = σ = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = 6(0 - 0.5)² + 3(1 - 0.5)² + (2 - 0.5)² = 1.5 + 0.75 + 2.25 = 4.5

σ = √(4.5/10) = 0.671

we compute the t-test statistic

t = (x - μ)/σₓ

x = sample mean difference = 0.50

μ = 0

σₓ = standard error of the sample mean = (σ/√n)

where n = Sample size = 10,

σ = Sample standard deviation = 0.671

σₓ = (0.671/√10) = 0.2122

t = (0.50 - 0) ÷ 0.2122

t = 2.356

3) checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 10 - 1 = 9

Significance level = 5% = 0.05

The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for t = 2.356, at 0.05 significance level, df = 9, with a one tailed condition) = 0.021441 = 0.0214

4) Alpha = significance level = 5% = 0.05

5) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.0214

0.0214 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.

Hope this Helps!!

Answer:

  yes, they are parallel; the general form equation differs only in the constant.

Step-by-step explanation:

Subtract y from the first equation and multiply by 2.

  y -y = 1/2x -y +3

  0 = x -2y +6

  x -2y +6 = 0 . . . . . put in general form

Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.

This means the lines are parallel.

Answer:

The total percentage increase in the country's population over the three year period is 7.6%.

Step-by-step explanation:

Let x be the original population of a country.

It is provided that the population increased by 3%, 2.6%, and 1.8% in three successive years.

Compute the population of the country after three years as follows:

[tex]\text{New Population}=\text{Origibal Population}\times I_{1}\%\times I_{2}\%\times I_{3}\%[/tex]

                         [tex]=x\times [1+\frac{3}{100}]\times [1+\frac{2.6}{100}]\times [1+\frac{1.8}{100}]\\\\=x\times 1.03\times 1.026\times 1.018\\\\=1.07580204\cdot x\\\\\approx 1.076\cdot x[/tex]

The new population after three years is 1.076 x.

Compute the total percentage increase in the country's population over the three year period as follows:

[tex]\text{Total Increase}\%=\frac{\text{New Population}\ -\ \text{Original Population}}{\text{Original Population}}\times 100[/tex]

                         [tex]=\frac{1.076x-x}{x}\times 100\\\\=0.076\times 100\\\\=7.6\%[/tex]

Thus, the total percentage increase in the country's population over the three year period is 7.6%.

Answer:

(2, -2)

Step-by-step explanation:

y = -2x + 2

y = 2x - 6

Solve by elimination (make sure they're in the same form)

2y = -4

y = -2

plug -2 into either equation for y and solve for x

-2 + 6 = 2x

4 = 2x

x = 2

Answer:

10/18

=5/9

pls mark as brainliest

Answer:

5/9

Step-by-step explanation:

6 red cards, 8 green cards and 4 blue cards =  18 total cards

not green cards = 6 red+ 4 blue = 10 cards

P( not green) = number not green / total

                      = 10/18

                      =5/9

Answer:

[tex]\theta=45^{\circ}[/tex]

Step-by-step explanation:

We are given that the equation of lines

[tex]x+\sqrt 3y=1[/tex]

[tex](1-\sqrt 3)x+(1+\sqrt 3)y=8[/tex]

According to question

The vector perpendicular to the lines is given by

[tex]i+\sqrt 3j[/tex] and [tex](1-\sqrt 3)i+(1+\sqrt 3)j[/tex]

Therefore, the  angle between two vectors is given by

[tex]cos\theta=\frac{a_1a_2+b_1b_2}{\sqrt{a^2_1+b^2_1}\sqrt{a^2_2+b^2_2}}[/tex]

Using the formula

[tex]cos\theta=\frac{1(1-\sqrt 3)+\sqrt 3(1+\sqrt 3)}{2\times 2\sqrt 2}[/tex]

[tex]cos\theta=\frac{1-\sqrt 3+\sqrt 3+3}{4\sqrt 2}=\frac{1}{\sqrt 2}[/tex]

[tex]cos\theta=cos 45^{\circ}[/tex]

[tex]\theta=45^{\circ}[/tex]

Hence, the acute angle between the lines is given by

[tex]\theta=45^{\circ}[/tex]

Answer:

100

Step-by-step explanation:

4 tens +  6 tens = 10 tens = 10*10 = 100

[tex]\text{Solve:}\\\\4(x-2+y)\\\\\text{Use the distributive property:}\\\\4x-8+4y\\\\\text{Since you can't simplify it any further, that'll be your answer}\\\\\boxed{4x-8+4y}[/tex]

Answer:

4x-8+4y

Explanation:

///

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?

1)Yes as the probability of six having the correct shape is not unusual

2)NO. as the probability of six having the correct shape is unusual

3)Yes as the probability of six having the correct shape is unusual

4) No. as the probability of six having the correct shape is not unusual

Solution:

If exactly 6 of the 10 have the right shape, it means that the probability of success for the sample is

6/10 = 0.6

Expressing the probability in terms if percentage, it becomes

0.6 × 100 = 60%

Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success for the population is 89.4%

Comparing both probabilities, the probability of only 6 having the right shape is unusual. Therefore, the correct option is

3)Yes as the probability of six having the correct shape is unusual

Answer:

Option B is correct

Step-by-step explanation:

Original expression is |8 - 1| = 7 = distance between number 1 and number 8

=> Option B is correct

Hope this helps!

The number line model that matches the expression |8 - 1| which is correct option(B)

The graph can be defined as a pictorial representation or a diagram that represents data or values.

The expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given the expression as |8 - 1|,

The value of the expression would give us 7. Meaning that the distance between coordinate 8 and 1 is 7 units.

The graphs given models the expression, |8 - 1|.

Option A, would match |-8 -1| = 5 units

Option B, would match |8 - 1| = 7 units.

Therefore, the answer is option (B).

Learn more about graph here :

https://brainly.com/question/16608196

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Answer:

Step-by-step explanation:

7w + 72 + 24w

31w + 72

Step-by-step explanation:

use distributive property to multiply x by 4x-5

[tex]4x ^{2} - 5[/tex]

Answer:

BRAINLEST

Step-by-step explanation:

[tex]4 { \times }^{2} - 5x[/tex]

this is the answer

Answer:

9x + 4x^2 - 5y

Step-by-step explanation:

It is given in the question that the length of a rectangular field is represented by the expression 14x - 3x^2 + 2y and width of the field by 5x - 7x^2 + 7y

Now we have to tell how much greater is the length of the field than the width.

That means length is greater than width and we have to subtract width from length.

Length - width = (14x - 3x^2 + 2y) - (5x - 7x^2+ 7y)

                        = 14x - 5x - 3x^2 + 7x^2 + 2y - 7y

                        = 9x + 4x^2 - 5y

Therefore expression which represents the difference between length and width of the field will be (9x + 4x^2 - 5y)

By 9x+4x²-5y length is greater than the width of a rectangle.

To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.

Given that, the length of rectangle is 14x-3x²+2y and width of a rectangle is 5x-7x²+7y.

To find how much greater is the length of the field than the width we need to subtract the width from the length, we get

14x-3x²+2y-(5x-7x²+7y)

= 14x-3x²+2y-5x+7x²-7y

= 9x+4x²-5y

Therefore, option A is the correct answer.

To learn more about the subtraction of expression visit:

https://brainly.com/question/12959016.

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"Your question is incomplete, probably the complete question/missing part is:"

The length of a rectangular field is represented by the expression14x-3x^2+2y. The width of the field is represented by the expression 5x-7x^2+7y. How much greater is the length of the field than the width?

A) 9x+4x^2-5y

B)9x-10x^2-5y

C)19x+4x^2+9y

D) 19x-10x^2+9y

Note: The first file attached contains the clear and complete question

Answer:

a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7

A(t) has a local maximum at t=7

A(t) has a local minimum at t=1

b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74

D(t) has a local maximum at t=1.59

D(t) has a local minimum at t=7.74

c) A(t) = (-t^3) + 8(t^2) -21t + 40

d) The water level in vat A is rising most rapidly at t = 4 hrs

e) 138 gallons

f) 18 gallons per hour

g) 98 gallons

Step-by-step explanation:

For clarity and easiness of expression, the calculations are handwritten and attached as files below.

Each step is neatly expressed and solutions to each part of the question are clearly written

Answer:

A

Step-by-step explanation:

The smaller negative integer is x.

The larger one is x+8, since they are 8 units apart.

The equation would be:

x*(x+8)=308

Let's simplify it by distributing.

x^2+8x=308

Subtract 308 from both sides.

x^2+8x-308=0

Therefore, the answer would be A.

Answer:

Step-by-step explanation: 6z=-2-10

6z= -12

z=-12/6

then z= -2

Answer:

1-20: Make it 0 units tall (change nothing)

21-40: Make it 1 unit tall

41-60: Make it 3 units tall

61-80: Make it 2 units tall

81-100: Make it 2 units tall

Step-by-step explanation:

1-20: (0 numbers)

21-40: 33 (1 number)

41-60: 43, 44, 52 (3 numbers)

61-80: 75, 79 (2 numbers)

81-100: 86, 89 (2 numbers)

Answer:

The age of the pottery bowl is 12,378.7 years

Step-by-step explanation:

The amount of C-14 after t yeas is given by the following equation:

[tex]N(t) = N(0)e^{-kt}[/tex]

In which N(0) is the initial amount and k is the decay rate.

In this question, we have that:

[tex]k = 0.0001[/tex]

So

[tex]N(t) = N(0)e^{-0.0001t}[/tex]

Age of the pottery bowl:

29% of its original amount of C-14. So we have to find t for which N(t) = 0.29N(0). So

[tex]N(t) = N(0)e^{-0.0001t}[/tex]

[tex]0.29N(0) = N(0)e^{-0.0001t}[/tex]

[tex]e^{-0.0001t} = 0.29[/tex]

[tex]\ln{e^{-0.0001t}} = \ln{0.29}[/tex]

[tex]-0.0001t = \ln{0.29}[/tex]

[tex]t = -\frac{\ln{0.29}}{0.0001}[/tex]

[tex]t = 12378.7[/tex]

The age of the pottery bowl is 12,378.7 years

Answer:

That can be factored as

(x -1  (1/3) ) * ( x +3) * (x -4/5)

and the zeroes are located at:

x = 1.33333333...   x = -3    and x = .8

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ f(x)=(x+3)(5x-4)(3x-4) \ \ \ }[/tex]

Step-by-step explanation:

We need to factorise the following function

[tex]f(x)=15 x^3+13 x^2-80 x+48[/tex]

-3 is a trivial solution, we can notice that f(-3)=0

so we can factorise by (x+3)

let s note a, b and c real and let s write

[tex]f(x)=15 x^3+13 x^2-80 x+48=(x+3)(ax^2+bx+c)[/tex]

[tex](x+3)(ax^2+bx+c) = ax^3+bx^2+cx+3ax^2+3bx+3c=ax^3+(b+3a)x^2+(3b+c)x+3c[/tex]

let s identify...

the terms in [tex]x^3[/tex]

   15 = a

the terms in [tex]x^2[/tex]

   13 = b + 3a

the terms in x

   -80 = 3b+c

the constant terms

   48 = 3c

so it comes, c=48/3=16, a = 15, b = 13-3*15=13-45=-32

so [tex]f(x)=(x+3)(15x^2-32x+16)[/tex]

[tex]\Delta=32^2-4*15*16=64[/tex]

so the roots of [tex](15x^2-32x+16)[/tex] are

[tex]\dfrac{32-8}{15*2}=\dfrac{24}{30}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]

and

[tex]\dfrac{32+8}{15*2}=\dfrac{40}{30}=\dfrac{20}{15}=\dfrac{4}{3}[/tex]

so [tex]f(x)=(x+3)(5x-4)(3x-4)[/tex]

the zeros are -3, 4/5, 4/3

Answer:

  61°

Step-by-step explanation:

The inscribed angle has half the measure of the central angle subtending the same arc (AC).

  ∠ADC = (∠ABC)/2 = 122°/2

  ∠ADC = 61°

Answer:

a) Within 260 grams and 340 grams.

b) 68%

c) 32%

d) 97.35%

Step-by-step explanation:

The empirical rule 68-95-99.7 for bell-shaped distributions tells us that:

a) The data that covers 95% of the organs is within 2 standard deviations (z=±2).

Then we can calculate the bounds as:

[tex]X_1=\mu+z_1\cdot\sigma=300+-2\cdot 20=300+-40=260 \\\\X_2=\mu+z_2\cdot\sigma=300+2\cdot 20=300+40=340[/tex]

b) We have to calculate the number of deviations from the mean (z-score) we have for the values X=280 and X=320.

[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{280-300}{20}=\dfrac{-20}{20}=-1\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{320-300}{20}=\dfrac{20}{20}=1\\\\\\[/tex]

As there are the bounds for one standard devaition, it is expected tht 68% of the data will be within 280 grams and 320 grams.

c) This interval is complementary from the interval in point b, so it is expected that (100-68)%=32% of the organs weighs less than 280 grams or more than 320 grams.

d) We apply the same as point b but with X=240 and X=340 as bounds.

[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{240-300}{20}=\dfrac{-60}{20}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{340-300}{20}=\dfrac{40}{20}=2\\\\\\[/tex]

The lower bound is 3 deviations under the mean, so it is expected that (99.7/2)=49.85% of the data will be within this value and the mean.

The upper bound is 2 deviations above the mean, so it is expected that (95/2)=47.5% of the data will be within the mean and this value.

Then, within 240 grams and 340 grams will be (49.85+47.5)=97.35% of the organs.