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ANEK [815]
3 years ago
6

What is the mean number of hours that high school students spend on homework per week? It is known that the standard deviation o

f the population is 2.2 hours. In a random sample of 40 students, it is found that they average 13 hours per week on homework.
a) What is the standard deviation for this sample?
b) What is the critical value for a 90% confidence interval?
c) What is the critical value for a 95% confidence interval?
Mathematics
1 answer:
viva [34]3 years ago
6 0
This may help you

it is given that the standard deviation  0.8, so we can use  the normal distribution critical value for the 95% confidence interval. 
<span>sample mean = 2.36 </span>
<span>standard deviation = 0.8 </span>
<span>standard error of mean = σ / √ n </span>
<span>standard error of mean = 0.8 / √ 50 </span>
<span>se = 0.8/7.0711 </span>
<span>standard error of mean 0.1131 </span>
<span>Confidence interval 2.36-(0.1131)(1.96) </span>
<span>and 2.36+(0.1131)(1.96) </span>
<span>95% confidence interval :(2.14, 2.58) </span>
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3 years ago
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vampirchik [111]
\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}h

Employ a standard trick used in proving the chain rule:

\dfrac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\cdot\dfrac{\sqrt{x+h}-\sqrt x}h

The limit of a product is the product of limits, i.e. we can write

\displaystyle\left(\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\right)\cdot\left(\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt x}h\right)

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For the leftmost limit, we make a substitution y=\sqrt x. Now, if we make a slight change to x by adding a small number h, this propagates a similar small change in y that we'll call h', so that we can set y+h'=\sqrt{x+h}. Then as h\to0, we see that it's also the case that h'\to0 (since we fix y=\sqrt x). So we can write the remaining limit as

\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan\sqrt x}{\sqrt{x+h}-\sqrt x}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{y+h'-y}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{h'}

which in turn is the derivative of \tan y, another limit you probably already know how to compute. We'd end up with \sec^2y, or \sec^2\sqrt x.

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\dfrac{\mathrm d\tan\sqrt x}{\mathrm dx}=\dfrac{\sec^2\sqrt x}{2\sqrt x}
7 0
3 years ago
Find the measure of XCY. PLEASE HELP ME AND SHOW WORK
Dovator [93]

Answer:

Measure of angle XCY is 60°.

Step-by-step explanation:

"Measure of all inscribed angles by the same arc in one segment of the circle are equal"

Using this property in the given circle,

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By substituting the value of 'x' in the measure of ∠XCY,

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             = 61 - 1

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Therefore, measure of angle XCY is 60°.

4 0
2 years ago
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