I have attached 3 different problems, please could you help. Thank you

Answer:

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214[/tex]

Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

This probability is 1 subtracted by the pvalue of Z when X = 66.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{66.5 - 66}{0.214}[/tex]

[tex]Z = 2.336[/tex]

[tex]Z = 2.336[/tex] has a pvalue of 0.99.

1 - 0.99 = 0.01

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Answer: statistical

Step-by-step explanation: A statistical – is a question that can be answered by collecting data and that anticipates variability in those data • Statistics – the science of collecting, reviewing, and analyzing data

Answer:

relative maximum: x = 1

relative minimum: x = 7

Step-by-step explanation:

Critical points:

Values of x for which f'(x) = 0.

Second derivative test:

For a critical point, if f''(x) > 0, the critical point is a relative minimum.

Otherwise, if f''(x) < 0, the critical point is a relative maximum.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = x^{3} - 12x^{2} + 21x - 8[/tex]

Finding the critical points:

[tex]f'(x) = 3x^{2} - 24x + 21[/tex]

[tex]3x^{2} - 24x + 21 = 0[/tex]

Simplifying by 3

[tex]x^{2} - 8x + 7 = 0[/tex]

So [tex]a = 1, b = -8, c = 7[/tex]

[tex]\bigtriangleup = (-8)^{2} - 4*1*7 = 36[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{36}}{2} = 7[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{36}}{2} = 1[/tex]

Second derivative test:

The critical points are x = 1 and x = 7.

The second derivative is:

[tex]f''(x) = 6x - 24[/tex]

[tex]f''(1) = 6*1 - 24 = -18[/tex]

Since f''(1) < 0, at x = 1 there is a relative maximum.

[tex]f''(7) = 6*7 - 24 = 18[/tex]

Since f''(x) > 0, at x = 7 there is a relative minumum.

Answer:

Los pinos ocupan [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.

Step-by-step explanation:

Una manera de resolver este problema es la siguiente:

[tex] \\ 1km^{2} = 1km * 1km = 1000m * 1000m = 1000000m^{2}[/tex]

[tex] \\ 2km^{2} = 2km * 1km = 2000m * 1000m = 2000000m^{2} = 2 * 10^{6}m^{2}[/tex]

En palabras, [tex] \\ 2km^{2} = 2000000m^{2}[/tex], o dos kilómetros cuadrados son iguales a 2 millones de metros cuadrados.

Sabemos que:

De esta manera, la parte que ocupan los pinos es el total del bosque menos el área ocupada por las hayas. Por lo tanto, el área ocupada por los pinos es:

[tex] \\ 2000000m^{2} - 380000m^{2}[/tex]

[tex] \\ 1620000m^{2}[/tex]

¿Cuántos metros cuadrados ocupan los pinos?

Los pinos ocupan, entonces, [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.

Answer: 268 hamburgers

Answer: 2 ÷ 17

Step-by-step explanation: When you have something in this form, a/b, it means the same thing as a divided by b.

So 2/17 means the same thing as 2 ÷ 17.

Answer:

[tex] y = -\frac{1}{3}x-2[/tex]

Step-by-step explanation:

From the table it is clear that the line is passing through the points [tex] (0,\: -2)= (x_1, \:y_1) \: \&\: (-6, \:0)=(x_2,\:y_2) [/tex]

(There are many other points in the table and any two of them can chosen as per our convenience)

Equation of line in two point form is given as:

[tex] \frac{y-y_1}{y_1 - y_2} = \frac {x-x_1}{x_1 - x_2} \\\\

\therefore \frac{y-(-2)}{-2 - 0} = \frac {x-0}{0 - (-6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{0+6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{6)} \\\\

\therefore 6(y + 2) = - 2(x)\\

\therefore 6y + 12 = - 2x \\

\therefore 6y = - 2x - 12\\\\

\therefore y = -\frac{2}{6}x-\frac{12}{6}\\\\

\huge \red {\boxed {y = -\frac{1}{3}x-2}} \\\\[/tex]

Answer:

  3x²

Step-by-step explanation:

The area is the product of the dimensions of the base:

  area = x(3x) = 3x²

Answer:

The correct answers are B, C, D, B

Step-by-step explanation:

These answers complete the statements that show the difference between the mathematical and reasonable ranges. Good luck! :)

B) Rational Numbers

C) 30,800

D) Real Numbers

B) 800

Correct on edge2020!

Answer:

BCDB

Step-by-step explanation:

Answer:

a) 0.0668

b) 0.3085

c) 0.6247

Question:

A population is normally distributed with μ = 100 and σ= 20.

a. Find the probability that a value randomly selected from this population will have a value greater than

130.

b. Find the probability that a value randomly selected from this population will have a value less than 90.

c. Find the probability that a value randomly selected from this population will have a value between 90

and 130.

Step-by-step explanation:

a) The probability that a value randomly selected from this population will have a value greater than 130 = P(X >130)

A z-score also referred to as a standard normal table shows the number of standard deviations a raw score lays either above or below the mean.

Let's determine the z-score using:

z = (x - µ)/σ

µ = 100

σ = 20

z = (130-100)/20

z = 30/20 = 1.5

The probability from the standard normal table associated with z = 1.50 is 0.4332. This is the area between z = 1.50 and the mean.

The total area under any normal curve is 1. Due to the fact that the normal curve is symmetric about the mean, the area on either sides of the mean is 0.5.

The desired probability = 0.5000 - 0.4332

= 0.0668

Find attached the diagram.

b) The probability that a value randomly selected from this population will have a value less than 90 = P(X<90)

Using the z-score formula:

z = (x - µ)/σ

z = (90-100)/20

z = (-10)/20 = -0.5

The probability from the standard normal table associated with

z = -0.50 is 0.1915. This is the area between z = -0.50 and the mean.

The desired probability = 0.5000 - 0.1915

= 0.3085

Find attached the diagram.

c) The probability that a value randomly selected from this population will have a value between 90 and 130 = P(90≤X≤130)

We earlier found the z score when P(X<90) = -0.5

And the probability associated with

z = -0.50 is 0.1915.

The z score when P(X>130) = 1.5

And the probability associated with z = 1.50 is 0.4332.

The desired probability is the addition of the two probabilities:

P(90≤X≤130) = 0.1915+0.4332

P(90≤X≤130) = 0.6247

Step-by-step explanation:

Replace x = 3

f(3) = 2(3) - 2

= 6 - 2

= 4

Answer:

f(3) =4

Step-by-step explanation:

f(x) = 2x - 2

Let x=3

f(3) = 2*3 - 2

     = 6-2

     = 4

Answer:

Step-by-step explanation:

the data is skewed left

The data in the given set is skewed towards left because the mean of the data is 7.5 and the data is not distributed symmetrically in the given set. Thus, the correct option is C.

Skewed data is the data which creates an asymmetrical, skewed curve on the graph scale. In statistics, the graph of a data set with normal distribution is symmetrical and has a bell-like shape. However, the skewed data has a tail on either side of the graph as well.

Skewness can be demonstrated on a bell curve when the data points are not distributed symmetrically to the left and right sides of the median on the curve. If the bell curve is shifted to the left or towards the right side, it is said to be skewed curve. The two halves of the distribution are not mirror images in the skewed curve because the data are not distributed equally on both sides of the distribution peak.

Therefore, the correct option is C.

Learn more about Skewed data here:

https://brainly.com/question/3907939

#SPJ2

Answer:

D. Parabola; 0°

Step-by-step explanation:

Answer:

Any values that is greater than 1/2.

Step-by-step explanation:

You have to form an inequality. Given that what values is added to c will satisfy that 3 - 5c is less than 1 - c :

[tex]3 - 5c < 1 - c[/tex]

Next, you have to solve :

[tex] - 5c + c < 1 - 3[/tex]

[tex] - 4c < - 2[/tex]

[tex]c > \frac{ - 2}{ - 4} [/tex]

[tex]c > \frac{1}{2} [/tex]

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Given:

Total number of glasses = 16

Number of glasses containing prune juice = 4

Number of glasses containing apple juice = 2

To find:  fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice

Solution:

A fraction refers to the parts of a whole. In a fraction, a top number is the numerator, and a bottom number is the denominator.

Number of glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = 16 - 4 - 2 = 10

Total number of glasses = 16

So,

Fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = [tex]\frac{10}{16}=\frac{5}{8}[/tex]

Answer:

Lauren is wrong

Step-by-step explanation:

1. Lauren is wrong

2. What’s the cost of the shirts before tax

Each shirt cost $15 and the total = $15 x 3 = $45

3. How much is the sales tax for all shirts

Sale tax for all shirts is $45 x 0.08 = $3.6

4. What is the total cost of the shirts, including tax?

Total cost  = $45 + $3.6 = $48.60

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

The table below contains the overall miles per gallon (MPG) of a type of vehicle. Complete parts a and b below.

28, 34, 28, 20, 21, 31, 28, 24, 34, 35 , 36, 26, 25, 20

a. Construct a 95% confidence interval estimate for the population mean MPG for this type of vehicle, assuming a normal distribution.

b. Choose the correct answer below.

A. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval.

B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval. This is the correct answer.

C.95 % of the sample data fall between the limits of the confidence interval.Your answer is not correct.

D. The mean MPG of this type of vehicle for 95?% of all samples of the same size is contained in the interval.

Solution:

a) Mean = (28 + 34 + 28 + 20 + 21 + 31 + 28 + 24 + 34 + 35 + 36 + 26 + 25 + 20)/14 = 27.86

Standard deviation = √(summation(x - mean)²/n

n = 14

Summation(x - mean)² = (28 - 27.86)^2 + (34 - 27.86)^2 + (28 - 27.86)^2 + (20 - 27.86)^2 + (21 - 27.86)^2+ (31 - 27.86)^2 + (28 - 27.86)^2 + (24 - 27.86)^2 + (34 - 27.86)^2 + (35 - 27.86)^2 + (36 - 27.86)^2 + (26 - 27.86)^2 + (25 - 27.86)^2 + (20 - 27.86)^2 = 399.7144

Standard deviation = √(399.7144/14) = 5.34

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 5.34

n = number of samples = 14

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 14 - 1 = 13

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.16

Margin of error = 2.16 × 5.34/√14

= 3.08

The confidence interval is 27.86 ± 3.08

b) B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval.

Answer:

Yes. Some examples are √2, √3, √5.

You better believe it !  In fact, if you don't count an infinite number of examples, you'll find that MOST of their square roots are irrational.

Let's examine the smallest 1,000 integers . . .

-- They're all rational numbers, but ...

-- only 31 of them have rational square roots !

Answer:

GRAPH OF 3X+2 IS 6

Step-by-step explanation:

Answer:

The graph below

Step-by-step explanation:

Answer:

a) Population of adults who watch local news

b) Population of adults who use cell phones or tablets.

c) They conducted a sample survey

d) I will find the results interesting.

I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.

Step-by-step explanation:

a) This finding is applicable to the population of adults who watch local news.

This is because the sample will be collected from the population of adults who watch local news to see the percentage that actually get those local news from their cell phones or tablet computers.

b) This finding is applicable to the population of adults who use cell phones or tablets.

The sample will be collected from the population of adults who use cell phones or tablets. A survey can now be carried out to find out what they use their phones or tablets for, whether to search for restaurants or get weather reports.

c) The Pew Researchers conducted a sample survey because a census data cannot contain the information about weather reports, local restaurants or news channel. Precise information can only be gotten from a sample survey.

d) Yes, I will. Having an idea of how large the population of those that search for local restaurants on phones and tablets will enable me to channel my publicity towards this media. I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.

Answer:

Step-by-step explanation:

A coin has two faces, a head (H) or tail (T). Tossing a coin twice in succession would give the following sample size;

                                 {HH, HT, TH, TT}

Given that: A = first toss is heads, B = second toss is heads, then:

i. P(A) = {HH, HT} = 2

ii. P(B) = {TH} = 1

iii. P(A∩B) = {HH} = 1

iv. P(B /A) = [tex]\frac{1}{2}[/tex]

Answer:

2.9 per hour

Step-by-step explanation:

Divide 69.9 by 24

Answer:

(a)77.4bpm

(b)Mean of Sample 1 = 70.3 beats per minute.  

Mean pulse of sample 2 = 70 beats per minute.

(c)

Step-by-step explanation:

(a)Population mean pulse.

The pulse of the nine students which represent the population are:

[tex]\text{Population Mean} =\dfrac{64+77+89+69+89+65+88+69+87}{9} \\=\dfrac{697}{9} \\\\=77.44[/tex]

The population mean pulse is approximately 77.4 beats per minute.

(b)Sample 1: {Janette,Clarice,Megan}

Mean of Sample 1

[tex]\text{Sample 1 Mean} =\dfrac{65+69+77}{3} \\=\dfrac{211}{3} \\\\=70.3[/tex]

Sample 2: {Janette,Clarice,Megan}

Mean of Sample 2

[tex]\text{Sample 2 Mean} =\dfrac{64+69+77}{3} \\=\dfrac{210}{3} \\\\=70[/tex]

The mean pulse of sample 1 is approximately 70.3 beats per minute.  

The mean pulse of sample 2 is approximately 70 beats per minute.

(c)

Step-by-step explanation:

We have,

If a quadratic equation with real coefficients has a discriminant of -36.

The general form of quadratic equation is :

[tex]ax^2+bx+c=0[/tex]

The discriminant of this equation is : [tex]D=b^2-4ac[/tex]

If D=0, it will have 1 real roots

If D>0, it will have 2 real roots

If D<0, it will have no real roots

We have,

D = -36 < 0, so, the quadratic equation will have no real roots.

Answer:

The Answer is 10, 50, and 54

Step-by-step explanation:

You want to figure this answer out by using the Pythagorean Theorem. If 10 squared plus 50 squared does not equal 54 squared, then those side lengths can not make a triangle.  

Answer:

117 units cubed.

Step-by-step explanation:

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

Answer:

117

Step-by-step explanation:

find all the shown surface area

Let the amount that Sky receives be S, and the amount that Natalia recieves be N.

[tex] \dfrac{s}{n} = \dfrac{6}{5} [/tex]

[tex]s = n + 3 \\ \\ \dfrac{n + 3}{n} = \frac{6}{5} \\ \\ 5n + 15 = 6n \\ \\ n = 15[/tex]

15 euros

Answer:

24% of those surveyed liked neither

Step-by-step explanation:

Set concepts:

We use set concepts to solve this question.

I am going to say that:

P(A) is the percentage of people that liked to swim.

P(B) is the the percentage of people that liked to run.

The percentage of people that liked at least one of these activities is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In which [tex]P(A \cap B)[/tex] is the probability that a person liked both these activities.

The percentage of people that liked neither is:

[tex]P = 1 - P(A \cup B)[/tex]

Of those surveyed, 58% said they liked to swim and 36% said they liked to run.

This means that [tex]P(A) = 0.58, P(B) = 0.36[/tex]

18% said they liked both swimming and running

This means that [tex]P(A \cap B) = 0.18[/tex]

What percent of those surveyed liked neither?

At least one:

[tex]P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76[/tex]

Neither:

[tex]P = 1 - P(A \cup B) = 1 - 0.76 = 0.24[/tex]

24% of those surveyed liked neither