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2 years ago

Form a sequence that has two arithmetic means between -1 and 59.

2 answers:

7 0

The formula for solving the problem is as follow:
an = a1 + (n - 1)d
Where:
n = number of figure in the sequence = 4
d = difference between successive number =?
a1 = -1
a4 = 59
Insert the given values into the formula,
59 = -1 + (4 - 1)d
59 = -1 + 3d
59 + 1 = 3d
60 = 3d
d = 60/3 = 20
Therefore, d = 20. This implies that, there is a difference of 20 between successive numbers.
The number sequence is as follow:
-1, 19, 39, 59.

Stels [109]2 years ago

7 0

<span><span>two arithmetic means between -1 and 59.
</span>b.-1, 19, 39, 59</span>

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Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st

Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)

b) n=523 rounded up to the nearest integer

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X=530$ represent the sample mean for the sample

$\mu$ population mean

s=70 represent the sample standard deviation

n=48 represent the sample size (variable of interest)

Confidence =95% or 0.995

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are df=n-1=48-1=47

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that $z_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$530-2.01\frac{70}{\sqrt{48}}=509.692$

$530+2.01\frac{70}{\sqrt{48}}=550.308$

So on this case the 95% confidence interval would be given by (509.592;550.308)

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

Assuming that $\hat \sigma =s$

And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ , replacing into formula (b) we got:

$n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523$

So the answer for this case would be n=523 rounded up to the nearest integer

3 0

2 years ago

Joan conducted a study to see how common binge drinking is on her college campus. She defined "frequent binge drinking" as havin

jenyasd209 [6]

Answer:

z = -1.66

Step-by-step explanation:

Z-statistic:

$z = \frac{X - p}{s}$

In which X is the found proportion.

p is the mean proportion.

$s = \sqrt{\frac{p(1-p)}{n}}$ is the standard error for the data.

Out of 593 students who replied to her survey, 64 fit this criterion.

This means that $X = \frac{64}{593} = 0.108$

She finds that the proportion of binge drinkers nationally is 13.1%.

This means that $p = 0.131$

Also

$s = \sqrt{\frac{0.131*0.869}{593}} = 0.014$

The z statistic for this data is

$z = \frac{X - p}{s}$

$z = \frac{0.108 - 0.131}{0.014}$

$z = -1.66$

6 0

2 years ago

A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of

rewona [7]

A margin of error means how much a prediction can be wrong. So if a prediction is 54% and the margin of error is 4%, then it can be wrong by 4 percent, so it could be 4 % less (50%) or more (58%).

Correct Answer;
X is the actual answer.
50%≤x≥58%
brainliest pls

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2 years ago

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To fit between two windows, the width of a bookshelf must be no greater than Six and one half feet. Mrs. Aguilar purchases a boo

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6 and a half feet is equal to 78 inches. If she buys a 77 inch shelf, there is 1 inch between the window and the shelf.

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2 years ago

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Tyra is training for a bicycle race. Each week she rides a total distance greater than 10 km and less than or equal to 30 km. If

atroni [7]

Our distance is x
We know each week she rides a total distance greater than 10 km and less than or equal to 30 km
We can write this like the following:
x > 10
x <= 30

It also tells us the distance is always an even number and a multiple of 3. Ask your self, what are some numbers between 10 and 30 and is a multiple of 3.

12, 18, 24 and 30

So the possible distances are 12, 18, 24, 30

Notice each number is an even number and you can divide the number by 3 evenly so they are numbers with 3 being a multiple.

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2 years ago