consider a population of voters. suppose that that there are n=1000 voters in the population, 30% of whom favor jones. identify the event favors jones as a success s. it is evident that the probability of s on trial 1 is 0.30. consider the event b that s occurs on the second trial. then b can occur two ways: the first two trials are both successes or the first trial is a failure and the second is a success. show that p(b) = 0.3

Answer:

Option B is not the most common correct choice.

Step-by-step explanation:

The multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E.

The probability that any of these five option is the correct answer is:

[tex]p=\frac{1}{5}=0.20[/tex]

A random sample of 400 multiple-choice questions on Advanced Placement exam are selected.

The results showed that 90 of the 400 questions having B as the answer.

To test the hypothesis that option B is more likely the correct answer for most question, the hypothesis can be defined as:

H₀: All the options are equally probable, i.e. p = 0.20.

Hₐ: Option B is more likely the correct option, i.e. p > 0.20.

Compute the sample proportion as follows:

[tex]\hat p=\frac{90}{400}=0.225[/tex]

The test statistic is:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.225-0.20}{\sqrt{\frac{0.20(1-0.20)}{400}}}= 1.25[/tex]

The test statistic is 1.25.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

[tex]p-value=P(Z>1.25)\\=1-P(Z<1.25)\\=1-0.89435\\=0.10565\\\approx 0.1057[/tex]

*Use a z-table.

The p-value is 0.1057.

The p-value of the test is quite large. Thus, the null hypothesis was failed to rejected.

Hence, it can be concluded that option B is not  the most common correct choice.

Testing the hypothesis, it is found that since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.

At the null hypothesis, it is tested if all of them are equally as likely, that is, the proportion of B is [tex]p = \frac{1}{5} = 0.2[/tex]. Thus:

[tex]H_0: p = 0.2[/tex]

At the alternative hypothesis, it is tested if B is more likely, that is, if the proportion of B is more than 0.2. Thus:

[tex]H_1: p > 0.2[/tex]

The test statistic is given by:

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

In which:

In this problem, the parameters are: [tex]p = 0.2, n = 400, \overline{p} = \frac{90}{400} = 0.225[/tex].

The value of the test statistic is:

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

[tex]z = \frac{0.225 - 0.2}{\sqrt{\frac{0.2(0.8)}{400}}}[/tex]

[tex]z = 1.25[/tex]

The p-value of the test is the probability of finding a sample proportion above 0.225, which is 1 subtracted by the p-value of z = 1.25.

Looking at the z-table, z = 1.25 has a p-value of 0.8944.

1 - 0.8944 = 0.1056.

Since the p-value of the test is of 0.1056 > 0.05, it does not provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely.

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Answer:

8 1/3

Step-by-step explanation:

2 1/2 * 3 1/3

Change each to an improper fraction

2 1/2  = (2*2 +1)/2 = 5/2

3 1/3 = (3*3+1)/3 = 10/3

5/2 *10/3 = 50/6

Divide the top and bottom by 2

25/3

Change to a mixed number

3 goes into 25    8 times with 1 left over

8 1/3

Answer:

28 or 29%

Step-by-step explanation:

There are 7 days total, 2 of which start with “S”, divide the 2 by 7 to get your percentage of 28-29%

The probability of picking a day that begins with the letter s is 2/7.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

There are seven days in a week, and two of them start with the letter s: Sunday and Saturday.

Now,

The probability of picking a day that begins with the letter s.

= 2/7

Or,

= 0.2857

Or,

= 0.2857 x 100%

= 28.57%.

Thus,

The probability of picking a day that begins with the letter s is 2/7.

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Answer:

Binomial probability distribution.

Step-by-step explanation:

For each watch, there are only two possible outcomes. Either it fails within 1 year of purchase, or it does not. The probability of a watch falling within 1 year of purchase is independent of other watches. So the type of of distribution will best model the number of watches out of the 15 sampled that fail within 1 year is the binomial probability distribution.

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.

Answer:

Step-by-step explanation:

Hello!

You need to construct a 95% CI for the population variance of the forces the safety helmets transmit to wearers.

The variable of interest is X: Force a helmet transmits its wearer when an external force is applied (pounds)

Assuming this variable has a normal distribution, the manufacturer expects it to have a mean of μ= 800 pounds and a standard deviation of σ= 40 pounds

A test sample of n=40 was taken and the resulting mean and variance are:

X[bar]= 825 pounds

S²= 2350 pounds²

To estimate the population variance per confidence interval you have to use the following statistic:

[tex]X^2= \frac{(n-1)S^2}{Sigma^2} ~~X^2_{n-1}[/tex]

And the CI is calculated as:

[[tex]\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}}[/tex];[tex]\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}}[/tex]]

[tex]X^2_{n-1;1-\alpha /2}= X^2_{39;0.975}= 58.1[/tex]

[tex]X^2_{n-1;\alpha /2}= X^2_{39;0.025}= 23.7[/tex]

[[tex]\frac{39*2350}{58.1}[/tex];[tex]\frac{39*2350}{23.7}[/tex]]

[1577.45; 3867.09] pounds²

Using a confidence level of 95% you'd expect that the interval [1577.45; 3867.09] pounds² contains the value of the population variance of the force the safety helmets transmit to their wearers when an external force is applied.

I hope this helps!

Answer:

3x√x²y, –12x√x²y, x√yx², 2√x²y. or on Edge is A,B,D,F

Step-by-step explanation:

Got 100% on edge...

Answer: The copy machine makes 171 copies in 4 minutes and 45 seconds.

Step-by-step explanation:

Let's dissect the question. The copy machine makes 36 copies per minute.

36 per min.

To see how many copies it makes in 4 minutes and 45 seconds, we multiply 36 * 4.75. 45 seconds is 3/4ths of a minute, or 0.75 of a minute.

[tex]36 * 4.75=171[/tex]

It makes 171 copies in 4 minutes and 45 seconds.

Answer:

2 seconds and 38 seconds

Step-by-step explanation:

h=-16t²-vot

1,200=-16t²-640t

turn this into standard form

16t²-640t+1200=0

now plug thes numbers into the quadratice formula

a 16 b -640 c 1200

solve with quadratic formula to get ≅2 and ≅38 seconds

Answer:

t≈2 seconds,t≈38 seconds

Step-by-step explanation:

h=−16t2+ v0t

Step 1. Solve the equation.

1,200= −16t^2+ 640t

We know the velocity, v0, is 640 feet per second.

The height is 1,200 feet. Substitute the values.

This is a quadratic equation. Rewrite it in standard form. Solve the equation using the quadratic formula.

ax^2 +   bx  +      c .   = 0

16t^2 −640t +  1,200 = 0

Identify the values of a, b, and c.

a=16,  b=−640, c=1,200

Write the quadratic formula.

t=−b± √b2−4ac‾‾‾‾‾‾‾‾

               2a

640+ √332,800‾‾‾‾‾‾‾‾   t= √640− √332,800‾‾‾‾‾‾‾

             32                                           32

Rewrite to show two solutions.

t=640+332,800‾‾‾‾‾‾‾‾√32,t=640−332,800‾‾‾‾‾‾‾‾√32

Approximate the answer with a calculator.

t≈2 seconds,t≈38 seconds

Step 2. Check the answer. The check is left to you.

Step 3. Answer the question.

The firework will go up and then fall back down. As the firework goes up, it will reach 1,200 feet after approximately 2 seconds. It will also pass that height on the way down at 38 seconds.

Answer:

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Everything has to add up to 90.

Add EVERYTHING together.

3x + 33

3x + 33 = 90

90 - 33 = 57

57 / 3 = 19

19 = x

19 x 2 = 38

38 - 8 = 30

Answer:

The answer for ∠CDF is 30°.

Step-by-step explanation:

It ia given that complemetary angle is 90° so we can make an expression in terms of x :

It ia given that complemetary angle is 90° so we can make an expression in terms of x :∠AFB + ∠BFC + ∠CFD = 90°

32° + (x+9)° + (2x-8)° = 90°

In order to find ∠CFD, we have to find the value of x first so we have to move all the like-terms to one side :

32° + x + 9° + 2x - 8° = 90°

2x + x = 90° - 32° - 9° + 8°

3x = 57°

Then divide both sides by 3 :

3x ÷ 3 = 57° ÷ 3

x = 19°

We have already found the value of x. Now, the question ask us to find ∠CDF, (2x-8)°. We just have to substitute x value into the expression :

Let x = 19,

∠CDF = 2x - 8

= 2(19) - 8

= 30°

Answer:

Whats on the list?????

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

1/6 * 3/6 (First roll has a one in 6 chance, second 3 in 6)

1*3 / 36 =

3 / 36 =

1/12

Answer:

B

Step-by-step explanation:

One-thirdx2y cm3 i got it right on edg

The volume of the pyramid with a square base of side x and height (y) is  (1/3)x²y cm³

Volume is the amount of space occupied by a three dimensional shape or object.

The area of the square base = x cm * x cm = x² cm²

The volume of the pyramid = (1/3) * area of square base * height = (1/3) * x² * y = (1/3)x²y cm³

The volume of the pyramid with a square base of side x and height (y) is  (1/3)x²y cm³

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Answer:

a. The percentage of all taxpayers who file electronically is 58%

b. 654 people used an accountant or professional tax preparer preparing the tax return

Step-by-step explanation:

According to the given data, in order to estimate the percentage of all taxpayers who file electronically, we would have to make the following calculation:

percentage of all taxpayers who file electronically=634×100%=0.58

                                                                                    1,091

Hence, the percentage of all taxpayers who file electronically is 58%

In order to calculate how many people used an accountant or professional tax preparer for preparing the tax return, we would have to make the following calculation:

people used an accountant or professional tax preparer= 60%×1,091=654

                                                                                                 100%

654 people used an accountant or professional tax preparer preparing the tax return.

Answer:

Correct Answer: CA larger sample size results in a smaller margin error, i.e. with a plant of 100 plots instead of 25, the margin error will be smaller.

Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

An agricultural researcher plants 25 plots with a new variety of yellow corn.

Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with unknown mean and standard deviation of 10.

We need to find a confidence interval with a smaller margin of error than the 90% confidence interval

n=25, x=150,s=10,a=0.95

Unknown mean u means we use t table.

[tex]150 ± t_{0.975} \frac{10}{\sqrt{25}}[/tex]

150±[tex]t_{0.975}[/tex]×2

Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error

Hence, option C is correct. Compute a 99% confidence interval rather than a 90% confidence interval, because a higher confidence level will result in a smaller margin of error

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Answer:

0.663

Step-by-step explanation:

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.

In this problem, we have that:

[tex]\mu = 138.5, \sigma = 29[/tex]

What proportion of cars spends between 120 and 180 seconds in Wendy's drive-thru?

This is the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 120. So

X = 180

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

[tex]Z = \frac{180 - 138.5}{29}[/tex]

[tex]Z = 1.43[/tex]

[tex]Z = 1.43[/tex] has a pvalue of 0.924

X = 120

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

[tex]Z = \frac{120 - 138.5}{29}[/tex]

[tex]Z = -0.64[/tex]

[tex]Z = -0.64[/tex] has a pvalue of 0.261

0.924 - 0.261 = 0.663

Final answer:

0.662 when rounded to three decimal places.

Explanation:

To determine the proportion of cars that spend between 120 and 180 seconds in Wendy's drive-thru, we can use the properties of the normal distribution. Given that the mean time is 138.5 seconds and the standard deviation is 29 seconds, we can calculate the corresponding z-scores for both 120 seconds and 180 seconds.

Firstly, calculate the z-score for 120 seconds:
z = (X - µ) / σ = (120 - 138.5) / 29 ≈ -0.6379.

Next, calculate the z-score for 180 seconds:
z = (X - µ) / σ = (180 - 138.5) / 29 ≈ 1.4310.

By looking up these z-scores in a standard normal distribution table, we find that:
P(Z < 1.4310) ≈ 0.9236
P(Z < -0.6379) ≈ 0.2616.

To find the proportion of times between 120 and 180 seconds, we subtract the smaller probability from the larger:
P(120 < X < 180) = P(Z < 1.4310) - P(Z < -0.6379) ≈ 0.9236 - 0.2616 = 0.6620.

Answer:

1/1000

Step-by-step explanation:

Answer:

(4,-4)

Step-by-step explanation:

Diagonals of a rectangle share a common midpoint

(4-6)/2 , (0-4)/2 = (-6+x)/2, (0+y)/2

-2 = -6 + x

x = 4

-4 = y

We determined the fourth point of a rectangle by ensuring that the sides of the rectangle are parallel to the axes and the sides are equal in length. The fourth point of the rectangle formed by the points (4,0), (-6,0), and (-6,-4) is (4,-4).

The fourth point of the rectangle should have the same x-coordinate as the point (4,0) and the same y-coordinate as the point (-6,-4). Therefore, the fourth point is (4,-4)

To better understand the reasoning, let's consider the points on a plane. We recall that rectangles have sides of equal length and parallel to the axes. Therefore, since the line connecting (4,0) and (-6,0) is parallel to the x-axis, the fourth point's x-coordinate has to be the same as the point on the opposite side of the rectangle, which is 4. Similarly, as the line connecting (-6,0) and (-6,-4) is parallel to the y-axis, the fourth point's y-coordinate has to equal the y-coordinate of the point on the opposite side (-6,-4), which is -4. Hence, the fourth point is (4,-4).

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Answer:

Expected number of matches that occur = 4 matches

Step-by-step explanation:

First of all, let X_i be the event that when we turn over card i if it matches the required cards face.

Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.

The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;

The expected number of matches when cards are drawn from a standard 52-card deck is 4.

We define a match for each card position as X_i = 1 if a match occurs, and X_i = 0 otherwise. The expectation E(X_i) for each card is 1/13 because the probability of the ith card being an i-matched card (Ace in the 1st position, Two in the 2nd position, and so on up to King in the 13th, then repeat with Ace) is 1/13.

Given there are 52 cards, each having the same pattern of matching, the expected number of matches is computed as:

E(X) = E(X_1 + X_2 + ... + X_52) = E(X_1) + E(X_2) + ... + E(X_52)

Since E(X_i) = 1/13 for all i:

E(X) = 52 * (1/13) = 4

Therefore, the expected number of matches is 4.

Answer:

a) MSE = 61.33

Forecast for 8th month = 15

b) MSE = 34.51

Forecast for 8th month = 18

c) The average method provides a better forecast because of its low MSE

Explanation:

Check the attached file for the solvings.

To answer this two-part question, you'll need to calculate the mean square errors (MSE) using two different forecasting methods: using the most recent value as a forecast and using the average of all data for a forecast. The one with lower MSE is the correct prediction. The forecast for the next month is always based on the previous value or average value depending on the method.

To answer this question, you need to understand how mean square error (MSE) and forecasting work. For (a), we use the last value as the forecast for the next value and compute MSE. For (b), we use the average of all data as the forecast for the next value and calculate the MSE. Finally, we compare which method gives a lower MSE, therefore better forecasting.

For (a), the forecast values would be the previous month's data, i.e., forecast for month 2 is 23, month 3 is 14 and so on. To calculate MSE, you subtract each monthly value from its forecast, square the result and find the average of these squares. The forecast for month 8 would be the value of month 7 which is 15.

For (b), you calculate the average of all the data available and use it as a forecast for all the next periods. The MSE and forecast for month 8 can be calculated in a similar manner as in (a).

In step (c), compare the MSE calculated in step (a) and step (b). A lower MSE indicates a better forecast and consequently represents an accurate choice for a predictive model.

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

The factors of 15 are numbers that can divide even through 15 without any remainders.

  These numbers are 1, 3, 5 and 15;

When we roll two fair dice once, there are about 36 possible out comes and this is the sample space of rolling this fair dice.

          1       2             3              4             5                6

1       (1, 1) (1, 2)         (1, 3)         (1, 4)   (1, 5)          (1, 6)

2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

The total that will give a factor of 15;

  (1, 2)  (2, 3)   (1, 4)    (2, 1)   (3, 2)      (4, 1)

Out of the 36 possible outcomes, we have 6 whose sum will give a factor of 15;

  Probability of this  = [tex]\frac{6}{36}[/tex]   = [tex]\frac{1}{6}[/tex]

Answer:

2.68% probability that inflation will be above 13% next year

Step-by-step explanation:

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.

In this problem, we have that:

[tex]\mu = 3.37, \sigma = 5[/tex]

If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year

This is the pvalue of Z when X = 13. So

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

[tex]Z = \frac{13 - 3.37}{5}[/tex]

[tex]Z = 1.93[/tex]

[tex]Z = 1.93[/tex] has a pvalue of 0.9732

1 - 0.9732 = 0.0268

2.68% probability that inflation will be above 13% next year

Answer:

[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]

And we can find this probability using the complement rule and the normal standard distirbution table or excel:

[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the annual inflation of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(3.37,5)[/tex]  

Where [tex]\mu=3.37[/tex] and [tex]\sigma=5[/tex]

We are interested on this probability

[tex]P(X>13)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X>13)=P(\frac{X-\mu}{\sigma}>\frac{13-\mu}{\sigma})=P(Z>\frac{13-3.37}{5})=P(Z>1.926)[/tex]

And we can find this probability using the complement rule and the normal standard distirbution table or excel:

[tex]P(Z>1.926)=1-P(Z<1.926)=1-0.9729=0.0271[/tex]

Answer:

You dont multiply anything, you just round

Step-by-step explanation:

basically, you round the 2.3 to the nearest whole number which is most likely 2 because 3 is under five so it doesnt round up

Answer:

x ≤-9/4

Step-by-step explanation:

x/3-x-1/2≥1

Multiply each side by 6 to get rid of the fractions

6(x/3-x-1/2)≥1*6

2x -6x -3≥6

Combine like terms

-4x-3≥6

Add 3 to each side

-4x-3+3≥6+3

-4x ≥9

Divide each side by -4, remembering to flip the inequality

-4x/-4 ≤9/-4

x ≤-9/4

On solving the inequality x/3 - x - 1/2 ≥ 1, we get x ≤ -3. Hence the correct option is A.

Solve the inequality: x/3 - x - 1/2 ≥ 1

Combine like terms: x/3 - (2x + 1)/2 ≥ 1

Get a common denominator: 2x/6 - 3(2x + 1)/6 ≥ 6/6

Simplify the equation: -4x - 3 ≥ 0

Solve for x: x ≤ -3

Answer:

A = 81 pi ft^2

Step-by-step explanation:

The area of a circle is found by

A = pi r^2

The radius is 9

A = pi 9^2

A = 81 pi ft^2

Answer:

3.8

Step-by-step explanation:

Answer:

Country B gaines 2 units of good X , per unit of Good Y sacrifised.

Step-by-step explanation:

Country B's production possibilities in form of goods (X,Y) are :

The country can produce 60 units of good X or 30 units of good Y, by complete specialisation in either good & not producing the other good.

The country has more (twice) advantage in producing good X. As, it can produce 2 times more good X, than good Y, from the same available resources.

If it decides to produce at point J, production specialising in Good X:    It will produce only good X, no units of Y. This implies that - it gains 2 units of good X per unit of good Y sacrifised, as per their production potential ratio (60:30)