step bye step problem

Answer:

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.

This means that:

[tex]p_h = \frac{230}{400} = 0.575, s_h = \sqrt{\frac{0.575*0.425}{400}} = 0.0247[/tex]

Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.

This means that:

[tex]p_n = \frac{25}{200} = 0.125, s_n = \sqrt{\frac{0.125*0.875}{200}} = 0.0234[/tex]

Distribution of the difference:

[tex]p = p_h - p_n = 0.575 - 0.125 = 0.45[/tex]

[tex]s = \sqrt{s_h^2+s_n^2} = \sqrt{0.0247^2 + 0.0234^2} = 0.034[/tex]

Confidence interval:

The confidence interval is:

[tex]p \pm zs[/tex]

In which

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

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower bound is [tex]0.45 - 1.96(0.034) = 0.3834[/tex]

The upper bound is [tex]0.45 + 1.96(0.034) = 0.5166[/tex]

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

Answer:

this should help you out

Answer:

So you're given that 7% is $126, and you have to find 100%. In order to do this you could set up proportions. 

1) 126/7=x/100

Next you can cross multiply and you'll get:

2) 12600=7x

Now divide each side by 7

3)12600/7=7x/7

And simplify

4)1800=x

Solution: $1800

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

The Range is the difference between the lowest and highest values (3, 34)

Answer:

31

Step-by-step explanation:

To find the range of the data set, simply subtract the smallest number from the biggest number.

34 - 3 = 31

Therefore, the range of the data set is 31.

The probability that a rental car delivered to the firm will need a tune-up is 0.05% and the conditional probability is 0.04%

The probability that a rental car delivered to the firm will need a tune-up

From the question, we have the following parameters that can be used in our computation:

Agency 1 = 0.42%,   Tune up from agency 1 = 0.08%

Agency 2 = 0.08%,   Tune up from agency 2 = 0.02%

Agency 3 = 0.5%,    Tune up from agency 3 = 0.02%

Using total probability, we have the following equation

P(tune-up) = P(tune-up | agency 1) * P(agency 1) + P(tune-up | agency 2) * P(agency 2) + P(tune-up | agency 3) * P(agency 3)

Substitute the known values in the above equation, so, we have the following representation

P(tune-up) = 0.08% * 0.42% + 0.02% * 0.08% + 0.02% * 0.5%

Evaluate the sum of products

P(tune-up) = 0.000452

Express as percentage and approximate

P(tune-up) = 0.05%

(b) The probability that it came from agency 2

This is a conditional probability, and it calculated as

P(Agency 2| Tune up) = P(Tune up and Agency 2)/P(Tune up)

Substitute the known values in the above equation, so, we have the following representation

P(Agency 2| Tune up) = (0.02% * 0.08%)/0.0452%

Evaluate

P(Agency 2| Tune up) = 0.0003539823

Express as percentage

P(Agency 2| Tune up) = 0.03539823%

Approximate

P(Agency 2| Tune up) = 0.04%

So, the probability is 0.04%

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Complete question

The members of a consulting firm rent cars from three rental agencies. It is estimated that 0.42 percent of cars come from agency 1, 0.08 percent of cars come from agency 2, and 0.5 percent of cars come from agency 3. It is also estimated that 0.08 percent of cars from agency 1 need a tune-up, 0.02 percent of cars from agency 2 need a tune-up, and 0.02 percent of cars from agency 3 need a tune-up. Answer the following questions, rounding your answers to two decimal places where appropriate.

(a) What is the probability that a rental car delivered to the firm will need a tune-up?

(b) If a rental car delivered to the firm needs a tune-up, what is the probability that it came from agency 2?

Answer: $32.75

Step-by-step explanation:

If each call costs $0.08 and you make 280 minutes worth of calls this month you'll have made $22.04 worth of phone calls plus the monthly access fee ($10.35) if you add both those fees you'll be left with a bill of $32.75.

I hope this answer helped you. :)

Answer:

$32.75

Step-by-step explanation:

10.35 + (0.08×280)

Answer:d

Step-by-step explanation:

Answer:

2/15 6/15 8/15 9/15 12/15

Step-by-step explanation:

Answer: 2/15, 6/15, 8/15, 9/15, 12/15.

Step-by-step explanation:

Just treat the denominators like they are not there for now, and treat the numerators like they are whole numbers and then rearrange:

8, 2, 9, 6, 12

Now rearrange from smallest to largest:

2, 6, 8, 9, 12

Now just put the denominators back in under the arranged numbers:

2/15, 6/15, 8/15, 9/15, 12/15

Words and their definitions:

Numerator: Top part of the fraction

Denominator: Bottom part of the fraction

Answer:

20.25

Step-by-step explanation:

6.75 times by 3 is 20.25

Answer: 10,000

Step-by-step explanation: here's how I got my answer:

Since we are finding the decrease from 2005-2015, we need to multiply 1/20 by 10, since the timespan is 10 years worth of decreasing.

So, 1/2 * 10 =1/2

So, since we have 1/2 as the overall decrease in the population within the 10 years, we divide 20,000 by 1/2 or 20,000 by 2, and we get 10,000. I hope this helps.

Answer:

The components that was having the second largest effect on population growth was deaths.

Step-by-step explanation:

In this question:

The largest the frequency(less time between each time, larger frequency), the higher effect of the component in population growth.

In this question:

Due to the rates, the effects on population growth, in descending order ir:

Birth - Deaths - Gain of one person - Migrants

So the components that was having the second largest effect on population growth was deaths.

Answer:

the remainder is not just added to the quotient. it becomes the numerator of a fraction that is added to the quotient. the correct answer is x-3- the process works for dividing any polynomial

Answer:

x=-5/2

Step-by-step explanation:

First you need to make 1/4x into x, to do that you multiply 4 on both side.

1/4x*4=-5/8*4

After multiplying 4 on both side you get:

x=-5/2

On solving the provided question we can say that by logarithm the statement is true he is short.

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

He is tall, or he is short and handsome

It is not true that he is short or not handsome

by logarithm,

the statement is true he is short.

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Answer:

pretty sure it's B. Let me know if im wrong

Step-by-step explanation:

Answer:

subtract 7

Step-by-step explanation:

y+7=18

You need to get the y by itself, so you subtract 7 to cancel it out.

y+7=18

 -7   -7

y=11

---

hope it helps

Answer:

The survey can be filled out in 120 different ways.

Step-by-step explanation:

The possible options are:

One professor from a set of four.

One meal from a set of five.

One weekend activity from a set of six.

Calculate the number of different ways the survey can be filled out if students select one from each category.

The multiplication of the number of possible outcomes for each trial. So

4*5*6 = 20*6 = 120

The survey can be filled out in 120 different ways.

9514 1404 393

Answer:

  B.  470 miles

Step-by-step explanation:

Using numbers rounded to the nearest 10, the remaining distance is ...

  1270 -420 -380 = 470 . . . . miles

Answer:

a. the player was traded in the last 5 years

For the NBA player's salary, the indicator (dummy) variables are:

These are variables that have one of two answers such as yes and no or positive and negative. They are represented as 0 or 1 for the most part.

A player being traded in the last 5 years can either be a yes or no response just like if a player has won an NBA championship or if they are on an All-Star team.

In conclusion, options A, B, and F are correct.

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Answer:

LKS

Step-by-step explanation:

just look at them

Answer:

LOJ is also DOL they the same

Answer:

64

Step-by-step explanation:

ˣ= 8

Since x² it means you have to multiply

8 two times

8 x 8= 64

Answer:

0.9 inches

Step-by-step explanation:

The sides of right triangles follow the Pythagorean Theorem:

a² + b² = c²

"a" and "b" are the two shorter sides and "c" is the hypotenuse, the longest side.

Let's plug in what we know.

a² + b² = c²

(1.2)² + b² = (1.5)²

Let's solve the exponents.

1.44 + b² = 2.25

Subtract 1.44 from both sides.

b² = 0.81

Take the square root of both sides.

√b² = √0.81

b = 0.9

The second side will be 0.9 inches.

Answer:

x + 23 = 65

x = 42

She had 42 buttons to begin with.

Answer:

the answer is

[tex] \sqrt{29} [/tex]

Answer:

4.5

Step-by-step explanation:

Answer:

[tex]\sqrt{20}[/tex], calculate this further on calculator if necessary

Step-by-step explanation:

The Pythagorean Theorem states that [tex]a^2 +b^2=c^2[/tex]

Plugged in, we get [tex]2^2+4^2=c^2[/tex]

4 + 16 = c^2

20 = c^2

c = [tex]\sqrt{20}[/tex]

The two scenarios that can be represented by a ratio 4:5 are

1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books

2. The ratio of marker to crayon , if there are 4 markers and 5 crayons. ( option A and D)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

For a scenario that will give ratio of 4:5, it means the first entity will be 4 and the second entity will be 5.

Therefore the two statements that obey this in the option are

1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books

2. The ratio of marker to crayon , if there are 4 markers and 5 crayons.

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