Consider a sample with data values of 10, 20, 12, 17, and 16. (a) Compute the mean and median. Mean = Median = (b) Consider a sample with data values 10, 20, 12, 17, 16, and 12. How would you expect the mean and median for these sample data to compare to the mean and median for part a (higher, lower, or the same)? The input in the box below will not be graded, but may be reviewed and considered by your instructor. Compute the mean and median for the sample data 10, 20, 12, 17, 16, and 12. If required, round your answers to one decimal place.

Answer:

- The probability that a bolt is too large for its nut = 0.00621

- The image of the drawing of this combined distribution is shown in the attached file to this solution.

Step-by-step explanation:

When independent, normal distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

For this question, the first distribution is the size of a nut, with mean 10 mm and a variance of 0.02

Second distribution is the size of a bolt, with mean 9.5 mm and a variance of 0.02.

The combined distribution is [size of nut − size of bolt]

Hence, λ₁ = 1, λ₂ = -1

μ₁ = 10 mm

μ₂ = 9.5 mm

σ₁² = 0.02

σ₂² = 0.02

Combined Mean = (1×10) + (-1×9.5) = 0.5 mm

Combined Variance = [(1)² × 0.02] + [(-1)² × 0.02] = 0.04

So, the combined distribution is also a normal distribution with a Mean of 0.5 mm and a variance of 0.04.

Standard deviation = √variance = √0.04 = 0.2 mm

The probability that a bolt is too large for its nut, [size of nut − size of bolt] ≤ 0, P(X ≤ 0)

To obtain this required probability, we first normalize/standardize 0 mm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (0 - 0.5)/0.2 = - 2.50

To determine the required probability

P(x ≤ 0) = P(z ≤ -2.50)

We'll use data from the normal probability table for these probabilities

P(x ≤ 0) = P(z ≤ -2.50) = 0.00621

The image of the drawing of this combined distribution is shown in the attached file to this solution.

Hope this Helps!!!

Answer:

rational

Step-by-step explanation:

rational + rational=rational

Answer:

d 0.0235

Step-by-step explanation:

We assume that the lifetime of the blenders follows a normal distribution, with mean of 36 months and standard deviation of 6 months.

We have to calculate the probability that the blenders have a lifetime lower than 24 months, and therefore apply the guarantee.

First, we calculate the z-score:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{24-36}{6}=\dfrac{-12}{6}=-2[/tex]

Then, the probability that the blenders lifetime is 24 or less is:

[tex]P(X<24)=P(z<-2)=0.023\\[/tex]

Answer:

-45

Step-by-step explanation:

-34+15=-19

-29-(-3)= -29+3= -26

-19 + -26 = -45

Answer:

-45

Step-by-step explanation:

-34 + 15 - 29 - (-3)

-34-29 +15+3

-63+18

18-63

-45

Answer:

<1=<5(alternative angle)

<3=<6(alternative angle)

<1+<2+<3=180(given)

<5+<2+<6=180(putting <1=<5 and <3=<5)

proved

Answer:

Step-by-step explanation:

let radius=r

height=h

dr/dt=1.6 in/s

dh/dt=-2.2 in/s

volume v=1/3 πr²h

dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]

when r=135 in

h=135 in

dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]

=1/3 π[135²(3.2-2.2)]

=1/3π135²×1

=6075 π in³/s

Answer:

25 and 36

Step-by-step explanation:

5^2=25

6^2=36

Answer:

Im feeling pretty today so imma go with C

Step-by-step explanation:

lol i took the test like about 2 days ago and i just checked my answers and C was right, good luck

Answer:

A. A larger sample size gives a narrower confidence interval.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

As the sample size increases(n increases), the margin of error decreases, given a narrower, more precise confidence interval.

So the correct answer is:

A. A larger sample size gives a narrower confidence interval.

Answer:

Richard works for $9 per hour

Step-by-step explanation:

Answer:

The answer is proportional. He makes 9$ an hour

Step-by-step explanation:

Your welcome

Answer:

150 minutes (2.5 hours)

Step-by-step explanation:

We must consider that the total time that the radio program lasted  represents the 100%.

Of that 100% we are told that 20% is dedicated to commercials. So the 30 minutes of commercials correspond to 20% of the air time, which can be represented in the following table:

Percentage of time             time

        20%                       ⇒     30min

and we are looking for how long the show was on the air (the 100%).

So updating the table( I will call x the total time on the air):

Percentage of time             time

        20%                       ⇒     30min

        100%                       ⇒     x

This reationship between three values can be solve by the rule of three: multiply the cross quantities on the table (100 by 30) and divide by the remaining amount (20):

x = 100*30 / 20

x= 3000 / 20

x = 150 minutes

The radio show was 150 minutes (2.5 hours) long.

Step-by-step explanation:

Y= x - 2. Y = 3x + 5

Putting value of y

x - 2 = 3x + 5

-2 - 5 = 3x - x

-7 = 2x

-7/2 = x

Putting value of x

Y = 3(-7/2) + 5

Y = - 10.5 + 5

Y = - 5.5

Answer:

[tex]\frac{6}{40}=\frac{3}{20}[/tex]

Step-by-step explanation:

The experimental probability is the number of times the desired result was obtained over the total number of times the experiment was carried out:

[tex]P=\frac{TimesTheEventOccurs}{TotalNumberOfTrials}[/tex]

In this case the Event we are looking for is rolling a 3 on the number cube.

The total number of trials is:

40

because the student rolls the cube 40 times.

and the times that he got the number 3 (the times the desired event occurs) is:

6

because he rolls a 3 on the number cube 6 times.

Thus our experimental probability to roll a 3 is:

[tex]P=\frac{6}{40}[/tex]

Answer:

[tex]x\in(1.146,\infty)[/tex]

Step-by-step explanation:

We are given an inequality

[tex]e^x>14[/tex]

We have to solve the given inequality.

Taking both side ln of given inequality

Then, we get

[tex]ln(e^x)>ln(14)[/tex]

[tex]xlne>1.146[/tex]

We know that

lne=1

Using the value

[tex]x>1.146[/tex]

[tex]x\in(1.146,\infty)[/tex]

Hence, the value of x is given by

[tex]x\in(1.146,\infty)[/tex]

Answer:

Step-by-step explanation:

The volume of a cone of height h and circular base of radius r, is [tex] V = \frac{\pi r^2 h}{3}[/tex]. In this case we have that [tex]V=72\pi[/tex].Then, we have that

[tex]72\pi = \frac{\pi r^2 h}{3}[/tex]

multiplying by 3 on both sides and dividing by [tex]\pi[/tex] we have that

[tex]216 = r^2\cdot h[/tex]

Suppose that we know the value of r, then we can find the value of h by solving h, that is

[tex] h = \frac{216}{r^2}[/tex].

So, by choosing any positive value of r, we can find the value for h. Note that if r=6, then [tex]h= \frac{216}{6^2} = 6[/tex]. This means that the amount of credit is infinite :)

Answer:

1 = 130° , 2 =50° , 3 = 85°, 4=45°

Step-by-step explanation:

1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}

2 = 180 - 1 { angles on a straight line equals 180}

= 180 -130 = 50°

4 = 180 - 135 = 45° { angles on a straight line equals 180}

3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}

3 = 135-50 = 85°

Note : sum of opposite interior angles equals external exterior angle, let's prove it:

If we look at the triangle at the bottom left, we have :

85, 45 and r { let's denote r as the missing angle}

So 85 + 45 + r = 180° { sum of angles of a triangle}

By simple arithmetic

r = 180 - ( 85+45) = 180 - 130 = 50°

but r + 4 = 180° { sum of angles in a straight line equals 180°}

4 = 180 - 50 = 130°

So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}

Answer:

a) 34.46% probability that her pulse rate is greater than 70 beats per minute.

b) 2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.

c) Because the underlying distribution(female's pulse rate) is normal.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

Distribution of females pulse rates:

Here, i suppose there was a typing mistake, since the mean and the standard deviation are lacking.

Also, the question c. only makes sense if the distribution is normal, so i will treat it as being.

I will use [tex]\mu = 68, \sigma = 5[/tex]. I am guessing these values, just using them to explain the question.

a. If 1 adult female is randomly selected, find the probability that her pulse rate is greater than 70 beats per minute.

This is 1 subtracted by the pvalue of Z when X = 70. So

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

[tex]Z = \frac{70 - 68}{5}[/tex]

[tex]Z = 0.4[/tex]

[tex]Z = 0.4[/tex] has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% probability that her pulse rate is greater than 70 beats per minute.

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute.

Now [tex]n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{70 - 68}{1}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30

The sample size only has to exceed 30 if the underlying distribution is normal. Here, the distribution of females' pulse rate is normal, so this requirement does not apply.

Answer:

x=-10

Step-by-step explanation:

x+8=-2

x=-10 (Subtract 8)

Answer:

-10

Step-by-step explanation:

1. Write it out.

x+8=-2

2. Get x by itself.

To do this, we have to move the 8, but to do that that we have to move it to the other side of the equation. Because the opposite of addition is subtraction, we have to subtract 8 by both sides.  x+8=-2

                                                                                        -8  -8

                                                                                      x=-10

And that's the answer! Hope this helped :)

Answer:

Option D: A hypothesis test regarding the difference between two population proportions from independent samples.

Step-by-step explanation:

A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the two population proportions if they are equal or not. It is appropriate under the condition that

The sampling method for each population is simple random sampling.

The samples are independent.

Each sample includes at least 10 successes and 10 failures.

Each population is at least 20 times as big as its sample.

Answer:

a. 0.1024

b. 0.8976

Step-by-step explanation:

The probability that x generators don't fail when they are needed follows a binomial distribution, because we have n identical and independent events (2 backup generators) with a probability p of success (1-0.32=0.68) and a probability q of failure (0.32).

So, the probability that x generator success are calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*q^{n-x}\\P(x)=\frac{2!}{x!(2-x)!}*0.68^{x}*0.32^{2-x}[/tex]

Then, the probability that both generators fail during a power outage is equal to the probability that 0 generators success. It is calculated as:

[tex]P(0)=\frac{2!}{0!(2-0)!}*0.68^{0}*0.32^{2-0}=0.1024[/tex]

At the same way, the probability of having a working generator in the event of a power outage is equal to the probability that at least 1 generator success. It is calculated as:

[tex]P(x\geq1)=P(1)+P(2) \\P(1)=\frac{2!}{1!(2-1)!}*0.68^{1}*0.32^{2-1}=0.4352\\P(2)=\frac{2!}{2!(2-2)!}*0.68^{2}*0.32^{2-2}=0.4624\\P(x\geq1)=0.4352+0.4624=0.8976[/tex]

This probability is not high enough for the hospital, both generators fail approximately the 10% of the time when needed.

The probability that the women's team experiences 2 or more concussions is 0.0013.

We are given that;

The concussion rate = 0.63 per 1,000 participation hours

Now,

The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space when these events occur with a known average rate and independently of the time since the last event.

The probability mass function of the Poisson distribution is given by:

[tex]$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$[/tex]

where X is the number of events occurring in the interval, k is a non-negative integer, and λ is the average rate of events per interval.

a. For collegiate men soccer players, the concussion rate is .41 per 1,000 participation hours.

Therefore, the average number of concussions per hour is λ = 0.41/1000 = 0.00041.

Let X be the number of concussions experienced by the men's team in an hour. Then X follows a Poisson distribution with parameter λ = 0.00041. We want to find P(X ≥ 2). Using the Poisson distribution formula,

[tex]$P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)$$= 1 - \frac{0.00041^0 e^{-0.00041}}{0!} - \frac{0.00041^1 e^{-0.00041}}{1!}$$= 1 - e^{-0.00041}(1 + 0.00041)$$\approx \boxed{0.0002}$[/tex]

b. For collegiate women soccer players, the concussion rate is .63 per 1,000 participation hours.

Therefore, the average number of concussions per hour is λ = 0.63/1000 = 0.00063.

Let Y be the number of concussions experienced by the women's team in an hour. Then Y follows a Poisson distribution with parameter λ = 0.00063. We want to find P(Y ≥ 2). Using the Poisson distribution formula,

[tex]$P(Y \geq 2) = 1 - P(Y < 2) = 1 - P(Y = 0) - P(Y = 1)$$= 1 - \frac{0.00063^0 e^{-0.00063}}{0!} - \frac{0.00063^1 e^{-0.00063}}{1!}$[/tex]

[tex]$= 1 - e^{-0.00063}(1 + 0.00063)$[/tex]

[tex]$\approx \boxed{0.0013}$[/tex]

Therefore, by poisson distribution formula answer will be 0.0013.

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Answer:

  2,856,271

Step-by-step explanation:

We presume your equation is intended to be ...

  P = 1,030,000(1.12)^t

To find the prediction in 9 years, put 9 where t is and do the arithmetic.

  P = 1030000(1.12^9) ≈ 2,856,271

In 9 years, the population is predicted to be about 2,856,271.

Answer:

To predict the population in nine years, substitute 9 for t in the equation and simplify:

P = 1,030,000(1.12)9

  = 1,030,000 ∙ 2.77

  = 2,853,100.

Step-by-step explanation:

Answer:

[tex]37[/tex]

[tex]77[/tex]

Step-by-step explanation:

[tex]17 \times 2 +3=37\\37 \times 2 +3=77[/tex]

Answer:

37   77

Step-by-step explanation:

2(17) + 3 = 37

2(37) + 3 = 77

Answer:

38.11% probability that the mean of her sample will be between 2700 and 2800 calories

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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 = 2760, \sigma = 500, n = 25, s = \frac{500}{\sqrt{25}} = 100[/tex]

Find the probability that the mean of her sample will be between 2700 and 2800 calories

This is the pvalue of Z when X = 2800 subtracted by the pvalue of Z when X = 2700.

X = 2800

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

By the Central Limit Theorem

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

[tex]Z = \frac{2800 - 2760}{100}[/tex]

[tex]Z = 0.4[/tex]

[tex]Z = 0.4[/tex] has a pvalue of 0.6554

X = 2700

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

[tex]Z = \frac{2700 - 2760}{100}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a pvalue of 0.2743

0.6554 - 0.2743 = 0.3811

38.11% probability that the mean of her sample will be between 2700 and 2800 calories

Answer:

Step-by-step explanation:

(x + 4)^2 - 2 = 7 simplifies to

(x + 4)^2 = 5

We must isolate x.  To do this, take the square root of both sides, obtaining:

x + 4 = ±√5

There are two roots/solutions.  They are:

x = -4 + √5 and x = -4 - √5            

You must include the square root operator (√).  Use "  ^  " to denote exponentiation.

The solutions to the given equation (x + 4)² - 2 = 7 when calculated are; 1 and 7

We are given the equation as;

(x + 4)² - 2 = 7

Add 2 to both sides to get;

(x + 4)² = 9

Find the square root of both sides to get;

x + 4 = ±3

Thus;

x = 3 + 4 and x = -3 + 4

x = 1 and 7

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Answer:

The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.

Answer:

8

Step-by-step explanation:

24+8=32 32 divided by 4 is 8

Answer: 8

Step-by-step explanation:

Plug in x as 2 and solve.

(12*2 + 8)/4

Start with parenthesis.

(32)/4

Now divide.

8

Answer:

C. Domain : {Gem, Hesh, Sam}

Range : {Gale, Abby, Beni}

B. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain.

Step-by-step explanation:

The figure of the mapping is attached below.

From the diagram, the domain for the relation is the set of Fathers:

{Gem, Hesh, Sam}

The range is the set of Sons:

{Gale, Abby, Beni}

The relation is a function. This is because each element in the range corresponds to exactly one element in the domain.

Answer:

A

Step-by-step explanation:

You can substitute 40 into c, work out the equation and you'll get $75 as the profit. Each candy bar is $2.5 so c would be the number of candy bars she sold.

Answer:

F(1) = 0

F(2) = -6 = 0 - 6 x 1 = F(1) - 6 x 1

F(3) = -12 = 0 - 6 x 2 = F(1) - 6 x 2

F(4) = -18 = 0 - 6 x 3 = F(1) - 6 x 3

...

F(n) = F(1) - 6 x (n - 1)

Hope this help!

:)