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4 years ago

Could someone PLEASE help?

1 answer:

4 0

Let X be a random variable representing the score of of student.
P(X ≥ 50) = 1 - P(X < 50) = 1 - P(z < (50 - 42)/8) = 1 - P(z < 1) = 1 - 0.84134 = 0.15866

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A manufacturer of piston rings for automobile engines frequently tests the width of the rings for quality control. Last week, a

kow [346]

Answer:

II and III

See explanation above

Step-by-step explanation:

When all other rings remain the same, which of the following conditions would have resulted in a wider interval than the one constructed?

I. A sample size of 20 with 95 percent confidence

II. A sample size of 15 with 99 percent of confidence

III. A sample size of 12 with 95 percent confidence

Previous concepts

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

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

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

The margin of error is given by:

$ME= t_{\alpha/2}\frac{s}{\sqrt{n}}$

I. A sample size of 20 with 95 percent confidence

The original sample size was 15, the degrees of freedom for the original interval would be n-1=14 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.14$

And then the Margin of error would be:

$ME=2.14 \frac{s}{\sqrt{15}}=0.553 s$

For the new sample size n=20 the degrees of freedom for the new interval interval would be n-1=19 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.09$

And then the Margin error would be:

$ME=2.09 \frac{s}{\sqrt{20}}=0.467 s$

So then we have a lower margin of error so then we will have a shorter interval

II. A sample size of 15 with 99 percent of confidence

The original sample size was 15, the degrees of freedom for the original interval would be n-1=14 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.14$

And then the Margin of error would be:

$ME=2.14 \frac{s}{\sqrt{15}}=0.553 s$

For the new interval the sample size n=15 the degrees of freedom for the new interval interval would be n-1=14 , the value for $\alpha=0.01$ and $\alpha/2=0.005$ and then the critical value is $t_{critc}=2.98$

And then the Margin error would be:

$ME=2.98 \frac{s}{\sqrt{15}}=0.769 s$

So then we have a greater margin of error so then we will have a wider interval. And this makes sense since with more confidence the interval needs to be wider.

III. A sample size of 12 with 95 percent confidence

The original sample size was 15, the degrees of freedom for the original interval would be n-1=14 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.14$

And then the Margin of error would be:

$ME=2.14 \frac{s}{\sqrt{15}}=0.553 s$

For the new interval the sample size n=12 the degrees of freedom for the new interval interval would be n-1=11 , the value for $\alpha=0.05$ and $\alpha/2=0.025$ and then the critical value is $t_{critc}=2.20$

And then the Margin error would be:

$ME=2.20 \frac{s}{\sqrt{12}}=0.635 s$

So then we have a greater margin of error so then we will have a wider interval.

5 0

4 years ago

2.1W iPod is used for 30 minutes. How much energy does it use

sesenic [268]

Answer:

The energy is 3780 joule

Step-by-step explanation:

we are given

Total power is 2.1 watt

so,

P=2.1 W

total time is 30 minutes

now, we can change in seconds

we know that

1 min =60 seconds

so, we get

$T=30\times 60sec=1800sec$

we know that

Energy = power*time

$E=P\times T$

we can plug value

$E=2.1\times 1800$

$E=3780$

So,

The energy is 3780 joule

6 0

3 years ago

How do you solve 135x42? (step by step please)

mojhsa [17]

Answer:

5,670

Step-by-step explanation:

how do you solve 135x42? (step by step please)

Answer :

= 135 x 42

= 5,670

3 0

3 years ago

Complete the steps for having the quadratic formula using the following ax^2+bx+c=0

melisa1 [442]

In order to solve am equation with the quadratic formula, we need to take the coefficients that are available and use them with the quadratic formula. Since there are no coefficients given here, we would just use the quadratic formula in its base form.

$\frac{-b +/- \sqrt{ b^{2} -4ac } }{2a}$

4 0

3 years ago

Which of the following is the standard form of the equation of a circle?

WITCHER [35]

The 1st one =no

2nd: YES

3rd : NO

4th yes

4 0

3 years ago