Find the probability of exactly two
successes in five trials of a binomial
experiment in which the probability of
success is 50%.
Round to the nearest tenth of a
percent.

Answer:

a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

b. Yes

c. The power of the test is 0.03836

d. The sample size can be considered adequate

Step-by-step explanation:

a. The given data in the study

Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0

Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8

Using the Average, Standard Deviation function from Microsoft Excel, we have;

The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22

The standard deviation for catalyst 1, σ₁ = 3.444416

The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42

The standard deviation for catalyst 2, σ₂ = 2.22401

The 95% confidence interval on the difference in mean is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

The critical-z for a 95% confidence interval = 1.96

Therefore, we have;

[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]

Therefore, we have;

The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

The test statistics is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

Therefore we have;

[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]

The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684

b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst

c. The power of the test

 The sample mean difference is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

Therefore, we have;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]

The z-value is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

μ₁ - μ₂ = 5

When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]

[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]

When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]

[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]

The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836

The power of the test = 0.03836

d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean

The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;

(-5.74, -0.66) which also contains -5 which is the difference in the population mean

Answer:

0.9644

Step-by-step explanation:

Answer:

Domain: (−∞,∞),{x|x∈R}

Step-by-step explanation:

the domain will be Domain: (−∞,∞),{x|x∈R} because

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Answer: Option C: (−∞,∞)

Step-by-step explanation:

answer is for plato

Answer:

g=1

Step-by-step explanation:

6g+3g=-3g+9+3g, add 3g to both sides and you get closer to the answer

Answer:

g=1

Step-by-step explanation:

solved and got the same answer

Answer: they are complementary but not necessarily congruent

Step-by-step explanation:

Answer:X=10

Step-by-step explanation: 3x-2=2x+8 If that's what you're looking for

Answer:

y = -3/4x - 7

Step-by-step explanation:

Slope intercept:

y - y1 = m(x - x1)

y + 1 = -3/4(x + 8)

y + 1 = -3/4x - 6

y = -3/4x - 7

Answer:

1) Congruent

2) Vertical angles

3) 12x - 18 = 8x + 10

4) x = 7

Step-by-step explanation:

1)

Congruent because they're vertical angles.

2)

Vertical angles

3)

12x - 18 = 8x + 10

4)

12x - 18 = 8x + 10

12x - 8x = 10 + 18

4x = 28

x = 7

Answer:

Cd equals the square root of 3

Answer: 2 square root 3

Step-by-step explanation:

other user's answer

Answer: x=3, elimination method

Step-by-step explanation:

x=3

-7x-2y=-13    ->  -7x-2y=-13

-(x-2y=11)      ->   -x+2y=-11

                        -----------------

                          -8x=-24

                              x = 3

elimination method

because you can easily eliminate one variable (y) using the elimination method

Answer:

55

Step-by-step explanation:

Answer:

5y+6

Step-by-step explanation:

-3 and 9 are like terms which can be simplified to 6.

Answer:

5y+6

Step-by-step explanation:

-3+5y+9

=-3+9+5y

=6+5y

=5y+6

Answer:

yeah my boy i think your right

Step-by-step explanation:

Answer:

By solving this equation for the variable ' d ', you learn how many days after you fill the tank you'll have to send somebody back to fill it again.

Step-by-step explanation:

Answer:

59/8

Step-by-step explanation:

Multiply the whole number by the denominator.

[tex]7 * 8 = 56[/tex]

Add the numerator to the product.

[tex]56 + 3 = 59[/tex]

Write the sum over the denominator.

[tex]\boxed{\frac{59}{8}}[/tex]

Hope this helps.

Answer:

If they water the plants in the garden together then it will take about 15 minutes because when they do it seperatly it takes about 30 minutes. So if they do it together, they are cutting work in half. And half of 30 is 15.

Step-by-step explanation:

32 rounded is 30.

25 rounded is 30.

30/ 2 = 15

Answer:

25/500 or 5% said 'other'

Step-by-step explanation:

55% = 275 (dog)

1/10 = 50 (cat)

0.3 = 150 (bird)

Total = 475

475 out of 500 (95%) gave an answer other than 'other'

Answer:

[tex]3.6 * 10^{3} \\\\[/tex]

Step-by-step explanation:

Answer:

Its only 5 point but ok

its $3.44 per quart

Step-by-step explanation:

Answer:

$ 56 .0000

Step-by-step explanation:

.......... ....... ....... ........ .....

Answer:

help him

Step-by-step explanation:

Paying a $2,500 down payment on an automobile would normally benefit Jim. He reduces the total amount of the loan for the vehicle he will need to take out by making a down payment, which reduces the cost of his monthly payments and the amount of interest he will have to pay over the life of the loan. Furthermore, having a down payment increases his chances of getting approved for a loan or receiving a cheaper interest rate.

A down payment is an upfront cash payment made when purchasing a significant ticket item like a car or a house. The down payment is often a proportion of the total cost of ownership and is made in order to lower the amount of financing required. Lower monthly payments or a shorter loan term are sometimes the outcome of a higher down payment.

A down payment is an initial up-front payment in part for the purchase of a large item or service, such as a car or a house. It is normally paid in cash or in the form of an equivalent at the time the transaction is completed. The balance of the payment is then financed by a loan of some kind.

Therefore, paying a $2,500 down payment on an automobile would normally benefit Jim.

Learn more about Down payment, here:

https://brainly.com/question/29397199

#SPJ2

Answer: your answer would be 6

8*3=24/4 and 24/4=6

Step-by-step explanation: Hope this help :D

Answer:

Because in order to find 3/4 of 8, you must solve for 8 * 3/4.

A helpful tip is that "of" is one of the giveaways of a multiplication problem. Others include but are not limited to, "multiply, " "product," "by," "times," "area," "twice," "double," "thrice," "triple," and "quadruple."

I would appreciate Brainliest, but no worries.

Answer:

54

Step-by-step explanation:

16 x 3 is 48 then plus 6 is 54

Answer:

Verifal angles I think but I'm not necessarily sure!!!

Answer: $1500 + 3% + $82,975= 84475.03

Step-by-step explanation:

Answer:

0.8 of a chocolate bar

Step-by-step explanation:

Bc 5 divided by 6 is 0.8

Answer:

f(x) = 4*(5/2)^x

Step-by-step explanation:

First, we know that our function has the points:

(0, 4)

(1, 10)

(2, 25)

The first one (0, 4) means that:

f(0) = 4.

Then you can evaluate the four given functions in x = 0 and see which ones meet this condition (have the outcome equal to 4)

Here we can discard the function f(x) = 15*x - 5 because:

f(0) = 15*0 - 5 = -5

Then this function is discarded.

Now let's look at the second point, (1, 10)

This means that f(1) = 10

Then you can evaluate the remaining functions in x = 1, and see if the outcome is equal to 10.

Here we can discard the first function f(x) = (x + 2)^2 because:

f(1) = (1 + 2)^2 = 3^2 = 9

So the output is not 10 as we wanted.

(while for the other two functions we have)

for f(x) = 6*x + 4

f(1) = 6*1 + 4 = 10

for f(x) = 4*(5/2)^x

f(1) = 4*(5/2)^1 = 4*(5/2) = (4/2)*5 = 10

Now we use the last point, (2, 25)

This means that when x = 2, the outcome needs to be equal to 25.

For the function f(x) = 6*x + 4 we have:

f(2) = 6*2 + 4 = 12 + 4 = 16

So we can discard this one.

Then we could conclude that the remaining option is the correct one, but let's ceck.

f(x) = 4*(5/2)^x

then for x = 2

f(2) = 4*(5/2)^2 = 4*(25/4) = 25

correct.

Then the correct option is f(x) = 4*(5/2)^x

Answer:

Option #2: 32 ÷2

Step-by-step explanation:

Take Note: There are 2 cups in a pint.

Since we are converting cups TO pints.... the number should (logically) be smaller. That eliminates the last two options.

Referring back to our note, it is only sensible to eliminate the first option since there are only 2 cups per pint, NOT 4.

In the end, you should have gotten option 2 which is 32÷2.

Answer:

2 : 5

Step-by-step explanation:

4/10 = 8.6/21.5 = 10/25 because all ratios equal 2/5

Answer:

2:5

Step-by-step explanation:

all the ratios are equal