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harina [27]
3 years ago
14

An advertising agency that manages a major radio station wants to estimate the mean amount of time that the station’s audience s

pends listening to the radio on a daily basis. From past studies, the standard deviation is assumed to be 20 minutes. What sample size is needed if the agency wants to have a 95% confidence interval with a margin of error equal to 5 minutes?
Mathematics
1 answer:
Kazeer [188]3 years ago
7 0

Answer:

n=(\frac{1.960(20)}{5})^2 =61.46 \approx 62

So the answer for this case would be n=62 rounded up to the nearest integer

Step-by-step explanation:

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 for the sample  

\mu population mean (variable of interest)

\sigma=20 represent the population standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

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

And on this case we have that ME =5 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 now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (b) we got:

n=(\frac{1.960(20)}{5})^2 =61.46 \approx 62

So the answer for this case would be n=62 rounded up to the nearest integer

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Is this correct? If not, please tell me the correct answer!!!
White raven [17]

Answer:

That is correct

Step-by-step explanation:

180° rotation about origin just means that you have to flip the pre-existing image across the x-axis

Good job!

3 0
3 years ago
Find the tangent of both angle A and angle B. Ignore what the picture says the numbers are the same.
Elena-2011 [213]
For the angle A we have:
 tan (A) = C.O / C.A
 tan (A) = 10/24
 Simplifying we have:
 tan (A) = 5/12
 For angle B we have:
 tan (B) = C.O / C.A
 tan (B) = 24/10
 Simplifying we have:
 tan (B) = 12/5
 Answer:
 
The tangent of angles A and B is given by:
 
tan (A) = 5/12
 
tan (B) = 12/5
4 0
3 years ago
According to data from a medical​ association, the rate of change in the number of hospital outpatient​ visits, in​ millions, in
GaryK [48]

Answer:

a) f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient​ visits, in​ millions, is given by:

f'(t)=0.001155t(t-1980)^{0.5}

a) To find the function f(t) you integrate f(t):

\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt

To solve the integral you use:

\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}

Next, you replace in the integral:

\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C

Then, the function f(t) is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient​ visits.

Hence C' = 264,034,000

The function is:

f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000

b) For t = 2015 you have:

f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7

3 0
3 years ago
Simplify. 5x^3/(7x^3+x^4)
Mashutka [201]
Hello,

\frac{5 x^{3} }{7 x^{3} + x^{4} } = \frac{5 x^{3} }{x^{3}(7+x) }=\frac{5} {7+x}

Answer Almost A with parenthesis 

5/(7+x)


6 0
3 years ago
How many distinct permutations are there of the letters of the word BOOKKEEPER?
emmainna [20.7K]
The letters of the word BOOKKEEPER can be arranged in 151,200 ways.

The group can be arranged in 8640 ways with all students of the same major together.

Explanation
There are 10 letters in the word bookkeeper.  There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.

An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
\frac{n!}{n_1!\times n_2!\times ... \times n_k!}
\\
\\=\frac{10!}{1!2!2!3!1!1!} = \frac{10!}{2!2!3!} = 151,200

Keeping all of the students of each major together makes each one essentially a "unit."  With this in mind, there are 3 units, that can be arranged in 3!=6 ways.

Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.

This gives us 6(6*2*120) = 8640 
7 0
3 years ago
Read 2 more answers
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