Assume that the amounts of weight that male college students gain their freshman year are normally distributed with a mean of u= 1.3 kg and a standard deviation of o= 4.8 kg. Complete parts (a) through (c) below.

a. If 1 male college student is randomly selected, find the probability that he gains 0 kg and 3 kg during freshman year.

b. If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.

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

Answer:

62

Step-by-step explanation:

divide lang yan.piste kasi bat kailangan 20 letters

Answer:

la respuesta es la D

Step-by-step explanation:

la velocidad es constante

In the given problem, we start by deriving expressions for the marginal propensity to consume (MPC), average propensity to consume (APC), marginal propensity to save (MPS), and average propensity to save (APS) using the consumption function and income function.

Deriving expressions for MPC, APC, MPS, and APS:

Using the consumption function C = C₁ + bY and the income function Y = C + S, we can derive the following expressions:

MPC (Marginal Propensity to Consume) = ΔC / ΔY

APC (Average Propensity to Consume) = C / Y

MPS (Marginal Propensity to Save) = ΔS / ΔY

APS (Average Propensity to Save) = S / Y

Deducing expressions for MPS and APS:

Given the consumption function C = 50 + 0.5Y, we can deduce the expressions for MPS and APS as follows:

MPS = ΔS / ΔY = Δ(Y - C) / ΔY = 1 - MPC

APC = C / Y = (50 + 0.5Y) / Y

APS = S / Y = (Y - C) / Y = 1 - APC

Confirming MPS > APS:

To confirm that MPS is greater than APS, we evaluate them at Y = 20:

MPS = 1 - MPC = 1 - 0.5 = 0.5

APC = C / Y = (50 + 0.5 * 20) / 20 = 52.5 / 20 = 2.625

APS = 1 - APC = 1 - 2.625 = -1.625

Since APS is negative and MPS is positive, it is evident that MPS > APS.

Derivatives of the given functions:

a) AC = Q² - 20Q + 120

The derivative of AC with respect to Q is: d(AC)/dQ = 2Q - 20

b) TR = 50Q - Q²

The derivative of TR with respect to Q is: d(TR)/dQ = 50 - 2Q

Determining intervals of increase or decrease:

a) AC = Q² - 20Q + 120

The quadratic function AC has a positive coefficient for the quadratic term (Q²), indicating a U-shaped curve. It opens upward, which means it is increasing for Q values less than the vertex of the parabola (Q = 10) and decreasing for Q values greater than the vertex.

b) TR = 50Q - Q²

The quadratic function TR has a negative coefficient for the quadratic term (Q²), indicating a downward-opening parabola. It is decreasing for all values of Q.

In summary, we derived expressions for MPC, APC, MPS, and APS using the consumption function and income function. We confirmed that MPS > APS by evaluating them at a given income level.

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Answer:

Radius is going to be 3 since half of the diameter is the radius.

Formula of a circumference you must remember:

2πr

(2 x pie (3.14 or 22/7) x your given radius or have of the diameter.

2 x 3.14 x 3 = 18.84

Adding a single subject that is way above the median to a sample with a very large sample size is likely to have a minimal impact on the overall distribution and statistics of the sample.

When the sample size is very large and the distribution of the statistic is approximately normal, the Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution, regardless of the underlying population distribution. This means that the sample mean is less sensitive to individual extreme values.

If a single subject is added to the sample that is way above the median, it will have a relatively small effect on the overall sample mean. This is because the impact of a single extreme value diminishes as the sample size increases.

When adding a single subject that is way above the median to a sample with a very large sample size, the effect on the overall distribution and statistics of the sample is expected to be minimal. The large sample size ensures that the sample mean remains robust and less influenced by individual extreme values. Therefore, the addition of a single subject with a very high value is unlikely to significantly alter the characteristics of the sample distribution or the calculated statistics such as the mean or standard deviation.

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28.26 sq. Ft is the area of the table top

(a) 0.3694 is the probability that the next charge will last less than 1.9 hours. (b) 0.2344 is the probability that the next charge will last between 2.9 and 4 hours. (c) 0.3830 the probability that the next charge will last more than 5 hours.

To solve these probabilities, we need to use the exponential probability distribution formula. The formula for the exponential distribution is:

[tex]P(X \leq x) = 1 - e^{-\lambda x}[/tex]

where,

λ is the rate parameter, and

x is the variable representing the duration.

Given that the average time a fully charged 6-volt laptop battery will operate a computer is 4.6 hours, we can find the rate parameter (λ) by taking the reciprocal of the average:

λ = 1 / 4.6

Now let's calculate the probabilities:

a) Determine the probability that the next charge will last less than 1.9 hours.

Using the exponential distribution formula:

[tex]P(X \leq 1.9) = 1 - e^{(-\lambda \times 1.9)}[/tex]

[tex]P(X \leq 1.9) = 1 - e^{(-\frac{1}{4.6} \times 1.9)}[/tex]

[tex]P(X \leq 1.9) = 1 - e^{(-0.4130)}[/tex]

P(X ≤ 1.9) ≈ 0.3694 (rounded to four decimal places)

Therefore, the probability that the next charge will last less than 1.9 hours is approximately 0.3694.

b) Determine the probability that the next charge will last between 2.9 and 4 hours.

Using the exponential distribution formula:

P(2.9 ≤ X ≤ 4) = P(X ≤ 4) - P(X ≤ 2.9)

[tex]P(2.9 \leq X \leq 4) = [1 - e^{(-\lambda \times 4)}] - [1 - e^{(-\lambda \times 2.9)}][/tex]

[tex]P(2.9 \leq X \leq 4) = [1 - e^{(-\frac{1}{4.6} \times 4)}] - [1 - e^{(-\frac{1}{4.6} \times 2.9)}][/tex]

P(2.9 ≤ X ≤ 4) ≈ 0.2344 (rounded to four decimal places)

Therefore, the probability that the next charge will last between 2.9 and 4 hours is approximately 0.2344.

(c) Determine the probability that the next charge will last more than 5 hours.

Using the exponential distribution formula:

P(X > 5) = 1 - P(X ≤ 5)

[tex]P(X > 5) = 1 - [1 - e^{(-\lambda \times 5)}][/tex]

[tex]P(X > 5) = 1 - [1 - e^{(-\frac{1}{4.6} \times 5)}][/tex]

P(X > 5) ≈ 0.3830 (rounded to four decimal places)

Therefore, the probability that the next charge will last more than 5 hours is approximately 0.3830.

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Answer:

174.95

Step-by-step explanation:

Volume=πr^2h

3.142 * (4.5÷2)^2 *11

=174.95

Answer:

Resto= $240.000

Step-by-step explanation:

Dada la siguiente información:

Cantidad total de dinero= $640.000

Costo de estudio= 3/8= 0,375

Costo de auto= 1/4= 0,25

Primero debemos calcular la cantidad total gastada, y después la diferencia:

Costo de estudio= 0,375*640.000= 240.000

Costo de auto= 0,25*640.000= 160.000

Gasto total= $400.000

Resto= 640.000 - 400.000

Resto= $240.000

Answer:

[tex] V_1 : V_2= 2197 : 729[/tex]

Step-by-step explanation:

Let the volumes of both the spheres be [tex] V_1, \:V_2[/tex] and their radii be [tex] r_1, \:r_2[/tex] respectively.

[tex] \huge r_1 : r_2= 13 : 9[/tex] (given)

[tex] \implies\huge \frac{r_1}{r_2}= \frac{13}{9}.....(1)[/tex]

[tex] \huge \frac{V_1}{V_2}=\frac{\cancel {\frac{4}{3} \pi} r_1^3}{\cancel {\frac{4}{3} \pi} r_2^3}[/tex]

[tex] \huge \frac{V_1}{V_2}=\frac{ r_1^3}{r_2^3}[/tex]

[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{ r_1}{r_2}\bigg) ^3..... (2)[/tex]

From equations (1) & (2), we have:

[tex]\huge \frac{V_1}{V_2}=\bigg(\frac{13}{9}\bigg) ^3[/tex]

[tex] \huge \frac{V_1}{V_2}=\frac{2197}{729}[/tex]

[tex] \huge \therefore V_1 : V_2= 2197 : 729[/tex]

Thus, the ratio of the volumes of two spheres would be 2197 : 729.

Answer:

2197:729

hope it helps

please mark brainliest

Answer:

You didnt write the options

Answer:

u=16

Step-by-step explanation:

64=4u

divide both sides by 4

16=u

Step-by-step explanation:

Area of Circle =

[tex]\pi {r}^{2} \\ = \pi( {1}^{2} ) \\ = 1\pi \\ = \pi {m}^{2} [/tex]

Answer: True False True true

Step-by-step explanation:

Answer:

true

false

true

true

Step-by-step explanation:

Answer: answer is D

Step-by-step explanation:

because science is more important than life

Answer:

we don't have any wasted metal and everything goes perfectly. In the real world, waste is inevitable.

Answer:

64 square cm

Step-by-step explanation:

(I pulled this out of the comments in case someone else needs this answer. Easier to see as an answer than as comments in the app)

Area 2 is easier, so we’ll start with that one. Area of a rectangle is length x width.

8 x 6 = 48 square cm

Area 1 is a triangle, so the formula is 1/2(base)(height). The height of the triangle is 8, because it’s the same as the base of the rectangle. The base of the triangle is 4, because we can subtract the 6 from the rectangle from the total side length of 10. Does that make sense?

So 1/2 (4)(8)= 1/2(32) = 16 square cm

Then we add 16 + 48 = 64 square cm

Answer:

For 5/11 shade in the third bubble (0.45 repeating)

Answer:

1 is E 2 is C

Step-by-step explanation:

15 is equal to or less than 6x

Answer:

$5829.57

Step-by-step explanation:

Annually compounding interest formula: [tex]PV(1+i)^t[/tex]

5000(1+.0525)^3

5829.567266

which rounds to: 5829.57

Answer:

The correct option is;

3. Theories need to undergo peer-review

Step-by-step explanation:

Within the scientific community, a theory has to be peer-reviewed by subject matter experts before it can be normally considered a valid theory. The peer-review process is one in which another scientific expert on the subject analyze, study, and repeat the experiments in the same conditions as stated in a publication submitted to a journal as a theory. The peer-review process aims to confirm the theory. A discovery which survives the peer review process will be considered a scientific theory and can then be expanded upon.

As of today, the team has played seven games, and "the team" has won them all.

This statement indicates that the team, whose specific name or identity is not provided, has achieved a perfect winning record by emerging victorious in all seven games they have participated in. The emphasis is on the collective success of the team rather than attributing the wins to any particular individual or naming the team itself. The phrase "has won them all" highlights the team's unbeaten streak and implies their dominance in the competition.

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A The null and alternative hypotheses in this case are:

Null hypothesis: H_o: μ ≥ 11

Alternative hypothesis: H_A: μ < 11

B We have statistically significant evidence to conclude that the setting results in less than 11% kernels unpopped.

C The t-statistic is -2.94.

d) The p-value is 0.004.

a) In this case, the company has made a Type I error. This is when the null hypothesis is rejected, even though it is true. In this case, the company would be rejecting the hypothesis that the setting results in less than 11% kernels unpopped, even though it is actually true. The consequence of this would be that the company would be losing money on refunds for popcorn that is not actually defective.

b) In order to answer this question, we need to calculate the t-statistic and the p-value.

The t-statistic is calculated as follows:

t = (x - μ) / (s / √n)

Substituting these values into the formula for the t-statistic, we get:

t = (6.7 - 11) / (3.5 / √8)

= -2.94

The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.

c) The t-statistic is -2.94.

d) The p-value is the probability of obtaining a t-statistic that is at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.004.The p-value is 0.004.

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Answer:

Step-by-step explanation:

The work done by an object can be found by using the formula

workdone = force × distance

From the question we have

workdone = 4.5 × 5

We have the final answer as

Hope this helps you

The "closure(A⁻)" of "subset-A" in a topological-space X is the intersection of all "closed-sets" containing A. It is smallest closed subset of X that contains A, means that if A⊂F⊂X and F is closed, then A⁻ is a subset of F.

In order to show that the closure(A⁻) is the smallest closed subset of X  which contains "A", we need to prove that if A ⊂ F ⊂ X and F is closed, then A⁻ ⊂ F,

We know that, A⁻ is intersection of all "closed-sets" containing A. Since F is "closed-set" which contains "A", it is one of the sets in the intersection defining A⁻. So, A⁻ is contained in F.

To show that A⁻ ⊂ F, we consider an arbitrary point x ∈ A⁻, which means that x is in the intersection of all closed sets containing A. Since, F is one such "closed-set" containing A, x must be in F as well.

Since x was an "arbitrary-point" in A⁻, we have shown that every point in A⁻ is also in F, So, A⁻ ⊂ F.

Therefore, we have proved that if A ⊂ F ⊂ X and F is closed, then A¯ ⊂ F.

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4020

you're supposed to multiply the length value by 1760

:P

A one-sided significance test gives a P-value of .02. From this we can conclude that we can reject the null hypothesis with 98% confidence.

Here’s why: In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic at least as extreme as the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the significance level (α), the null hypothesis can be rejected. Conversely, if the p-value is greater than the significance level, there is insufficient evidence to reject the null hypothesis. Since a one-sided significance test was performed, we are only interested in the probability that the test statistic will fall in one tail of the distribution.

Thus, the p-value is the probability of obtaining a test statistic as extreme as the observed value in one tail of the distribution. If the p-value is .02, this means that there is a 2% chance of obtaining a test statistic as extreme or more extreme than the observed value if the null hypothesis is true. Since the p-value is less than the standard significance level of .05, we can reject the null hypothesis with 98% confidence. This is because we can be 98% confident that the true population parameter falls in the alternative hypothesis range.

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Answer:

$1.25

Step-by-step explanation:

10/8 =1.25

Answer:

$1.25

Step-by-step explanation:

just divided 10 with 8

Characteristic 'c' using a 64-bit long real equivalent decimal number -147 with mantissa 'f' = 0.1484375, the number can be expressed as -1.48 x 10^2. The characteristic 'c' is the exponent of the power of 10. Therefore, the characteristic 'c' is -2.

The scientific notation representation of a real number is given by 'm x 10^c', where 'm' is the mantissa and 'c' is the characteristic. In this case, we have a 64-bit long real equivalent decimal number -147 with mantissa 'f' = 0.1484375. The number can be written as -1.48 x 10^2.

To determine the characteristic 'c', we look at the exponent of the power of 10. In this case, the exponent is 2. However, since the number is negative, the characteristic is also negative. Therefore, the characteristic 'c' is -2.In summary, for the given number -147 with mantissa 0.1484375, the characteristic 'c' is -2.

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The sample proportion is calculated by dividing the number of individuals who believe it is the responsibility of the federal government (493) by the total number of adult Americans surveyed (1050).

a) For the 95% confidence interval, we use the formula: Sample proportion ± Z * (Standard error). The value of Z is determined by the desired confidence level. In this case, for a 95% confidence level, Z is the critical value corresponding to a two-tailed test. By plugging in the values, we can calculate the lower and upper limits of the interval.

b) Similarly, for the 99% confidence interval, we use the same formula but with the appropriate critical value for a 99% confidence level.

Using Minitab Express or statistical tables, we can find the critical values and compute the confidence intervals.

Hence, the 95% confidence interval represents our level of confidence that the true proportion of adult Americans who believe it is the responsibility of the federal government to provide healthcare coverage lies within the reported interval. Similarly, the 99% confidence interval provides a higher level of confidence in capturing the true proportion.

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The joint PMF for X, Y is given by the following table:

x\y 5/128   9/128   1/64   5/32   9/32   1/16   15/128   27/128   3/64

The joint probability mass function (PMF) of two discrete random variables is a function that maps each pair of outcomes of the random variables to a probability. In particular, the joint PMF gives the probability that the random variables take a certain pair of values on each trial. Therefore, we have to find the probability that the random variables X and Y take each of the six possible values.

Therefore, the joint PMF for X, Y is given as follows:

P(X = -1, Y = -1)

= P(X = -1)P(Y = -1)

= (1/8)(5/16)

= 5/128

P(X = -1, Y = 0) = P(X = -1)P(Y = 0)

= (1/8)(9/16)

= 9/128

P(X = -1, Y = 1) = P(X = -1)P(Y = 1)

= (1/8)(1/8)

= 1/64

P(X = 0, Y = -1) = P(X = 0)P(Y = -1)

= (1/2)(5/16)

= 5/32

P(X = 0, Y = 0) = P(X = 0)P(Y = 0)

= (1/2)(9/16)

= 9/32

P(X = 0, Y = 1) = P(X = 0)P(Y = 1)

= (1/2)(1/8)

= 1/16

P(X = 1, Y = -1) = P(X = 1)P(Y = -1)

= (3/8)(5/16)

= 15/128

= (3/8)(9/16)

= 27/128

P(X = 1, Y = 1) = P(X = 1)P(Y = 1)

= (3/8)(1/8)

= 3/64

Therefore, the joint PMF for X, Y is given by the following table:

x\y 5/128   9/128   1/64   5/32   9/32   1/16   15/128   27/128   3/64

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