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As sample size increases, which of the following is true for a t-distribution-Distribution will get taller and SD will increase
-distribution sill get taller and SD will decrease
-distribution will get shorter and SD will decrease
Distribution will get shorter and SD will increase

Answers

Answer 1

Answer:

Answer:

Distribution will get taller and SD will decrease.

Step-by-step explanation:

Sample Size and Standard Deviation:

In a t-distribution, sample size and standard deviation are inversely related.

A larger sample size results in decreased standard deviation and a smaller sample size will result in increased standard deviation.

Sample Size and Shape of t-distribution:

As we increase the sample size, the corresponding degree of freedom increases which causes the t-distribution to like normal distribution. With a considerably larger sample size, the t-distribution and normal distribution are almost identical.

Degree of freedom = n - 1

Where n is the sample size.

The shape of the t-distribution becomes more taller and less spread out as the sample size is increased

Refer to the attached graphs, where the shape of a t-distribution is shown with respect to degrees of freedom and also t-distribution is compared with normal distribution.

We can clearly notice that as the degree of freedom increases, the shape of the t-distribution becomes taller and narrower which means more data at the center rather than at the tails.

Also notice that as the degree of freedom increases, the shape of the t-distribution approaches normal distribution.

Answer 2

Answer:

Final answer:

In a t-distribution, as the sample size increases, the distribution becomes 'shorter', and the standard deviation decreases following the law of large numbers. The increased sample size reduces variability and introduces less deviation from the mean.

Explanation:

As the sample size increases for a t-distribution, the distribution tends to approach a normal distribution shape, which means the distribution will get 'shorter'. Additionally, the standard deviation (SD) would generally decrease as the sample size increases. This is due to the fact that when sample size increases, a smaller variability is introduced, hence less deviation from the mean.

To illustrate, imagine rolling a dice. If you roll it a few times, you may end up with quite a bit of variation. If you roll it a hundred times, however, the numbers should average out closer to the expected value (3.5 for a six-sided dice), and the standard deviation (a measure of variability) would decrease.

In conclusion, when the sample size increases, a t-distribution will get 'shorter' and SD will decrease. This concept is often referred as the law of large numbers.

Learn more about t-distribution here:

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Solve the equation:a+20=11

A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =

Answers

Answer:

a) $(dB)/(dt) = (5\pi)/(4.2) \cdot \cos \left(2\pi\cdot (t)/(4.2) \right)$ , b) $(dB)/(dt)\approx 5.595$

Step-by-step explanation:

a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:

$(dB)/(dt) = \left((2\pi)/(4.2) \right)\cdot 0.25\cdot \cos (2\pi\cdot (t)/(4.2))$

$(dB)/(dt) = (5\pi)/(4.2) \cdot \cos \left(2\pi\cdot (t)/(4.2) \right)$

b) The rate of increase after one day is:

$(dB)/(dt) = (5\pi)/(4.2) \cdot \left(2\pi \cdot (1)/(4.2) \right)$

$(dB)/(dt)\approx 5.595$

HELP 100 PointsIf △NMK ≅ △TRP, then answer the following questions:
a. Complete the congruence statement: △MNK ≅ △_______
b. What side is congruent to ≅ ______
c. Solve for x. _____

Answers

The given statements to be completed are completed as follows;

A) △MNK ≅ △RTP

B) TR ≅ NM

C) x = 7

We are given that;

△NMK ≅ △TRP

This means that Triangle NMK is congruent to Triangle TRP.

A) The naming of △NMK is now △MNK. Thus, we have to now re-name Triangle TRP to match the naming of △MNK. Thus;

△MNK ≅ △RTP

B) From the 2 given triangles, we can see that TR and NM are the same length and also perpendicular lines.

Thus they are congruent to each other and as such;

TR ≅ NM

C) Since TR and NM are congruent to each other. Then;

TR = NM

Thus;

3x - 1 = 20

3x = 20 + 1

3x = 21

x = 21/3

x = 7

Read more at; brainly.com/question/13547762

Answer:

A-△MNK ≅ △RTP

B- TR≅NM

C- X=7

Step-by-step explanation:

I did the assignment loves.

Please I need help I dont know what to do

Answers

Answer:

Equation::2n-4=18::N=11

Step-by-step explanation:

Add 4 to both sides leaving you with this::2n=22

2.Then divide 22 by 2 and get n=11

3.So, N=11

In determining automobile-mileage ratings, it was found that the mpg (X) for a certain model is normally distributed, with a mean of 33 mpg and a standard deviation of 1.7 mpg. Find the following:__________. a. P(X<30)
b. P(28c. P(X>35)
d. P(X>31)
e. the mileage rating that the upper 5% of cars achieve.

Answers

The upper 5% of cars have a mileage rating of 35.805 mpg

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given; mean of 33 mpg and a standard deviation of 1.7

a) For < 30:

z = (30 - 33)/1.7 = -1.76

P(x < 30) = P(z < -1.76) = 1 - 0.8413 = 0.0392

b) For < 28:

z = (28 - 33)/1.7 = -2.94

P(x < 28) = P(z < -2.94) = 0.0016

c) For > 35:

z = (35 - 33)/1.7 = 1.18

P(x > 35) = P(z > 1.18) = 1 - P(z < 1.18) = 1 - 0.8810 = 0.119

d) For > 31:

z = (31 - 33)/1.7 = -1.18

P(x > 31) = P(z > -1.18) = 1 - P(z < -1.18) = 0.8810

e) The upper 5% of cars achieve have a z score of 1.65, hence:

1.65 = (x - 33)/1.7

x = 35.805 mpg

The upper 5% of cars have a mileage rating of 35.805 mpg

Find out more on z score at: brainly.com/question/25638875

Answer:

a) P(X < 30) = 0.0392.

b) P(28 < X < 32) = 0.2760

c) P(X > 35) = 0.1190

d) P(X > 31) = 0.8810

e) At least 35.7965 mpg

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

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 question, we have that:

$\mu = 33, \sigma = 1.7$

a. P(X<30)

This is the pvalue of Z when X = 30. So

$Z = (X - \mu)/(\sigma)$

$Z = (30 - 33)/(1.7)$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

Then

P(X < 30) = 0.0392.

b) P(28 < X < 32)

This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 28. So

X = 32

$Z = (X - \mu)/(\sigma)$

$Z = (32 - 33)/(1.7)$

$Z = -0.59$

$Z = -0.59$ has a pvalue of 0.2776.

X = 28

$Z = (X - \mu)/(\sigma)$

$Z = (28 - 33)/(1.7)$

$Z = -2.94$

$Z = -2.94$ has a pvalue of 0.0016.

0.2776 - 0.0016 = 0.2760.

P(28 < X < 32) = 0.2760

c) P(X>35)

This is 1 subtracted by the pvalue of Z when X = 35. So

$Z = (X - \mu)/(\sigma)$

$Z = (35 - 33)/(1.7)$

$Z = 1.18$

$Z = 1.18$ has a pvalue of 0.8810.

1 - 0.8810 = 0.1190

P(X > 35) = 0.1190

d. P(X>31)

This is 1 subtracted by the pvalue of Z when X = 31. So

$Z = (X - \mu)/(\sigma)$

$Z = (31 - 33)/(1.7)$

$Z = -1.18$

$Z = -1.18$ has a pvalue of 0.1190.

1 - 0.1190 = 0.8810

P(X > 31) = 0.8810

e. the mileage rating that the upper 5% of cars achieve.

At least the 95th percentile.

The 95th percentile is X when Z has a pvalue of 0.95. So it is X when Z = 1.645. Then

$Z = (X - \mu)/(\sigma)$

$1.645 = (X - 33)/(1.7)$

$X - 33 = 1.645*1.7$

$X = 35.7965$

At least 35.7965 mpg

WHAT IS THE SLOPE OF THE LINE
6X + 3Y = 18?

Answers

Answer:

−2

Step-by-step explanation:

Using the slope-intercept form, the slope is −2 .

It’s -2 and the y intercept is (0,6)

Which of the following expressions is equal to 5^6/ 5^2?1.) 5×5×5

2.) 1/5×5×5×5

3.) 5×5×5×5

4.) 3

Answers

The value of the expression 5⁶ / 5² will be 5 x 5 x 5 x 5. Then the correct option is C.

What is the value of the expression?

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expression is given below.

⇒ 5⁶ / 5²

Simplify the expression, then the value of the expression will be

⇒ 5⁴

⇒ 5 x 5 x 5 x 5

The value of the expression 5⁶ / 5² will be 5 x 5 x 5 x 5. Then the correct option is C.

More about the value of expression link is given below.

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Answer:

Step-by-step explanation:

When dividing exponents you subtract the top exponent from the bottom exponent so you would have 6-2 which is 4. Answer 3 is the only one that has 4 5's in the numerator.

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