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julz338
24.03.2020 •
Mathematics
A simple random sample of 35 colleges and universities in the United States has a mean tuition of $17,700 with a standard deviation of $10,300. Construct a 95% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole number.
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Ответ:
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $14,288 and $21,112.
Step-by-step explanation:
Sample size greater than 30, which means that we use the normal distribution to find the interval.
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so ![z = 1.96](/tpl/images/0561/2382/45e33.png)
Now, find M as such
In which
is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 17700 - 3412 = $14,288
The upper end of the interval is the sample mean added to M. So it is 17700 + 3412 = $21,112.
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $14,288 and $21,112.
Ответ:
Value of x in given equation
is -52.
Option B
Step-by-step explanation:
We have, the following equation as One-third x minus two-thirds = negative 18 , i.e.
.
In order to solve this, lets simplify the above equation:
⇒![\frac{x}{3} - \frac{2}{3} = -18](/tpl/images/0540/4801/ef96a.png)
⇒![\frac{x-2}{3} = -18](/tpl/images/0540/4801/7b251.png)
⇒![x-2 = -18(3)](/tpl/images/0540/4801/0156c.png)
⇒![x-2 = -54](/tpl/images/0540/4801/59b74.png)
⇒![x = -54 +2](/tpl/images/0540/4801/48737.png)
⇒![x = -52](/tpl/images/0540/4801/271e1.png)
∴ Value of x in the equation One-third x minus two-thirds = negative 18 i.e.
is -52. And so, correct option is B.