The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean

Answer:

A 90% confidence interval for the mean mathematics SAT score is (440, 478).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645*\frac{116}{100} = 19[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 459 - 19 = 440

The upper end of the interval is the sample mean added to M. So it is 459 + 19 = 478

A 90% confidence interval for the mean mathematics SAT score is (440, 478).

The 90% confidence interval for the SAT score is between 440 and 478.

mean (μ) = 459, standard deviation (σ) = 116, sample (n) = 100, confidence = 90% = 0.90

α = 1 - C = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05

The z score of α/2 is equal to the z score of 0.45 (0.5 - 0.05) which is equal to 1.645.

The margin of error (E) is given by:

[tex]E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.645*\frac{116}{\sqrt{100} } =19[/tex]

The confidence interval = μ ± E = 459 ± 19 = (440, 478)

The 90% confidence interval for the SAT score is between 440 and 478.

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Answer:

2/1

Step-by-step explanation:

So you want to find a point where the line crosses a intersection near perfectly, point A (1,3) and then a second point, B (2,5)

and then you count up from point a, on the Y axis until you are even with the second point, that number is your RISE

it is 2

then you just count over to point B from that spot where you counted up. RUN TO IT

1

so it is 2/1 or just 2

((point (0,1) would have worked too))

Answer:

c

Step-by-step explanation:

Answer: d) all of the above

Step-by-step explanation:

A Hamiltonian circuit is where you follow the path of the circuit touching EVERY VERTEX only ONE time.

Notice that each path given allows every vertex to be touched and each vertex is touched only once.

Therefore, all the options given are valid paths for a Hamiltonian circuit.

Answer: 10units^2

Step-by-step explanation:

You can find the area of the trapezoid by multiplying the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then dividing by 2.

The larger base is 2+2+4=8

so

A=(2+8)*2/2

=10

Answer:

Step-by-step explanation:

a) Confidence interval for the difference in the two proportions is written as

Difference in sample proportions ± margin of error

Sample proportion, p= x/n

Where x = number of success

n = number of samples

For the girls,

x = 60

n1 = 80

p1 = 60/80 = 0.75

For the boys

x = 80

n2 = 120

p2 = 80/120 = 0.67

Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.8 = 0.2

α/2 = 0.2/2 = 0.1

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.1 = 0.9

The z score corresponding to the area on the z table is 1.282. Thus, z score for confidence level of 80% is 1.282

Margin of error = 1.282 × √[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]

= 1.282 × √0.00418625

= 0.081

Confidence interval = 0.75 - 0.67 ± 0.081

= 0.08 ± 0.081

b) The formula for determining the standard error of the distribution of differences in sample proportions is expressed as

Standard error = √{(p1 - p2)/[(p1(1 - p1)/n1) + p2(1 - p2)/n2}

Therefore,

Standard error = √{(0.

75 - 0.67)/[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]

Standard error = √0.08/0.00418625

Standard error = 4.37

c) the difference in the probability between that girls prefer math more and boys prefer math more is

0.75 - 0.67 = 0.08

Answer:

a) The third quartile Q₃ = 56.45

b) Variance [tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Step-by-step explanation:

Given that :

[tex]Q_1[/tex]  =  30.8

Median [tex]Q_2[/tex] =  48.5

Mean  = 42

a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :

[tex]SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}[/tex]

[tex]-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}[/tex]

[tex]-0.38Q_3 + 11.704 = Q_3 +30.8 - 97[/tex]

[tex]1.38Q_3 = 77.904[/tex]

Divide both sides by 1.38

[tex]Q_3 = 56.45[/tex]

b) The objective here is to determine the approximate value of the variance;

Using the relation

[tex]SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}[/tex]

[tex]-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}[/tex]

[tex]-0.38= \dfrac{(-19.5) }{\sigma}[/tex]

[tex]-0.38* \sigma = {(-19.5) }{}[/tex]

[tex]\sigma =\dfrac {(-19.5) }{-0.38 }[/tex]

[tex]\sigma =51.32[/tex]

Variance =  [tex]\sigma^2 =51.32^2[/tex]

[tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Answer:

A. 1/2

Step-by-step explanation:

For 6 to become 3 and 12 to become 6, the (6,12) is being multiplied by 1/2.

Answer:

Step-by-step explanation:

The scale factor is from (6, 12) to (3, 6) is a.

1/2(6) = 3

1/2(12)= 6

Answer:

a)

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Step-by-step explanation:

a)

Given data population proportion 'p' = 19% =0.19

                                                          q  = 1-p = 1- 0.19 =0.81

Given  two people are randomly​ selected

 Given n = 2

Let 'X' be the random variable in binomial distribution

[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]

The probability that both will be hopelessly romantic is

                   [tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]

                     P(X = 2)   = 1 × 0.0361

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 1-P(x<1)

                            = 1 - ( p(x =0)

                            = [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]

                           = 1 - (0.81)²

                           = 1 -0.6561

                           = 0.3439

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Answer:

1 acre

Step-by-step explanation:

Answer:

B. (x - 8)(x - 5)

Step-by-step explanation:

If you plugged in x = 5 into the 2nd equation, you would see that you would be multiplying by 0, which would turn everything zero.

Answer:

95040 ways

Step-by-step explanation:

If we have 12 players, but of those 12 only 5 can be on the playing field, since there are only 5 positions, to know the different ways to assemble the team, we must calculate them by means of permutations, when n = 12 and r = 5.

nPr = n! / (n-r)!

replacing:

12P5 = 12! / (12-5)!

12P5 = 95040

In other words, there are a total of 95040 ways of assembling the equipment.

Answer:

left, if looking from person's point of view

Step-by-step explanation:

Answer:

It would be A

Step-by-step explanation:

If you cut off the overlapping cubes, you get the image on A.

Answer:

Step-by-step explanation:

x • (x - 5) • (x - 7)

Answer:

x(x-5)(x-7)

Step-by-step explanation:

x³ - 12x² + 35x

x(x² - 12x + 35)

x(x-5)(x-7)

Answer:

z = 1.645 should be used.

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].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].

z = 1.645 should be used.

Answer:

2,009.6 inches³

Step-by-step explanation:

The formula for the volume of a cylinder:

V = πr²h

Let's substitute into the given equation:

V = πr²h

V = (3.14)(8²)(10)

Solve:

V = (3.14)(8²)(10)

V = (3.14)(64)(10)

V = (200.96)(10)

V = 2,009.6

Therefore, the volume of the cylinder is 2,009.6 cubic inches.

Answer:

A) 0.28

B) 0.615

C) 0.26

Step-by-step explanation:

We are given;

Probabilities of customers using regular gas:P(A1) = 40% = 0.4

Probabilities of customers using plus gas: P(A2) = 35% = 0.35

Probabilities of customers using premium gas: P(A3) = 25% = 0.25

We are also given with conditional probabilities of full gas tank:

P(B|A1) = 40% = 0.4

P(B|A2) = 80% = 0.8

P(B|A3) = 70% = 0.7

A) The probability that next customer will requires extra unlead gas(plus gas) and fill the tank is:

P(A2 ∩ B) = P(A2) × P(B|A2)

P(A2 ∩ B) = 0.35 × 0.8

P(A2 ∩ B) = 0.28

B)The probability of next customer filling the tank is:

P(B) = [P(A1) • P(B|A1)] + [P(A2) • P(B|A2)] + [P(A3) • P(B|A3)]

P(B) = (0.4 × 0.4) + (0.35 × 0.8) + (0.25 × 0.7)

P(B) = 0.615

C)If the next customer fills the tank, probability of requesting regular gas is;

P(A1|B) = [P(A1) • P(B|A1)]/P(B)

P(A1|B) = (0.4 × 0.4)/0.615

P(A1|B) = 0.26

Answer:

35.2% probability that the sample mean will be 246 pages 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 = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61[/tex]

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{246 - 245}{2.61}[/tex]

[tex]Z = 0.38[/tex]

[tex]Z = 0.38[/tex] has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

Answer:

0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 155, p = 0.59[/tex]

So

[tex]\mu = E(X) = np = 155*0.59 = 91.45[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{155*0.59*0.41} = 6.12[/tex]

Probability that at least 91 out of 155 students will pass their college placement exams.

Using continuity correction, this is [tex]P(X \geq 91 - 0.5) = P(X \geq 90.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 90.5. So

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

[tex]Z = \frac{90.5 - 91.45}{6.12}[/tex]

[tex]Z = -0.155[/tex]

[tex]Z = -0.155[/tex] has a pvalue of 0.4384

1 - 0.4384 = 0.5616

0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.

Answer:

  B.  g(x)

Step-by-step explanation:

g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.

f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.

g(x) has the smallest minimum value

Answer:

$ 2263

Step-by-step explanation:

In this case to calculate the standard error of the mean, we only need the standard deviation (sd) and the number of the random sample (n).

sd = 13000

n = 33

SE = sd / (n ^ (1/2))

replacing:

SE = 13000 / (33 ^ (1/2))

SE = 2263.01

What the standard error of the mean for a random sample of 33 first-year lawyers means is $ 2263

The standard error of the mean is $2263

Since here are 310 first-year lawyers in a particular metropolitan area with an average starting salary of $156,000 and a standard deviation of $13,000.

So, the standard error is

[tex]= 13000 \div (33 ^ {(1\div 2))}[/tex]

= 2263.01

Therefore, we can conclude that The standard error of the mean is $2263

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Answer:

  10

Step-by-step explanation:

The two marked angles are a linear pair, so have a sum of 180°.

  (2m +10) +(5m +100) = 180

  7m +110 = 180 . . . . . . . collect terms

  7m = 70 . . . . . . . . . . . . subtract 110

  m = 10 . . . . . . . . . . . . . divide by 7

Answer:

math papa look on that website

Step-by-step explanation:

Answer:

99.85

Step-by-step explanation:

$99.85\text{ %}$

Notice that 52 inches is three standard deviations less than the mean. Based on the Empirical Rule, 99.7% of the yearly snowfalls are within three standard deviations of the mean. Since the normal distribution is symmetric, this implies that 0.15% of the yearly snowfalls are less than three standard deviations below the mean. Alternatively, 99.85% of the yearly snowfalls are greater than three standard deviations below the mean.

Answer:

At least 832 teenargers must be interviewed.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval

At least n teenargers must be interviewed.

n is found when M = 0.1.

We have that [tex]\sigma = 1.12[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.1 = 2.575*\frac{1.12}{\sqrt{n}}[/tex]

[tex]0.1\sqrt{n} = 2.575*1.12[/tex]

[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}[/tex]

[tex]n = 831.7[/tex]

Rounding up

At least 832 teenargers must be interviewed.

Answer:

The other number is 25

See explanation below

Step-by-step explanation:

The question is incomplete. Since we were not given the area or the answer to the multiplication of the two numbers, I would show you how to multiply two 2-digit numbers using the area model.

Let's assume we want to find the area model of 27 and 25.

We would write the multiplicands(the two digit numbers) in expanded form as tens and ones.

So, 27 becomes 20 and 7

25 becomes 20 and 5.

Then draw a box that is 2 by 2 grid ( 2 rows and 2 columns)

Then multiply the 1st column by the 1st row, 2nd column by 2nd row. Afterwards sum the values obtained together.

For the question: 25×27

20×20, 20×5, 20×7, 5÷7

400, 100, 140, 35

Their sum = 400 + 100+ 140 +35

= 675

See attachment for diagram.

In this question only one of the numbers is given. The area of the two numbers wasn't given.

Assuming the area of the two numbers was given and one if the numbers was also given, we would apply area model of division.

Example: Area of the both numbers = 675, the other number given = 27. Find the other number.

The area model of solving division is gotten from finding the area of a rectangle.

Since Area of a rectangle = Length × Width

Then the the value of length would be greater than value of breadth.

675÷27 = 25

So break it down to 20 and 5. Hence You divide first by 20 in first column. Then divide the remainder (135) by 5 in second column.

See diagram for explanation

Answer:

26

Step-by-step explanation:

Answer: 10.5 to 11.5 inches

Answer:

10.5 to 11.5 inches

Step-by-step explanation:

Answer: 30 for addition and 2376 for multipaction

Step-by-step explanation: Depending on how what algebraic expression.

Answer:

B on edge 2022

Step-by-step explanation: