Answer:
The correct option is (a) 0.9780.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
![\mu_{\hat p}=p](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%3Dp)
The standard deviation of this sampling distribution of sample proportion is:
![\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
As the sample selected is quite large, i.e. <em>n</em> = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
![\mu_{\hat p}=p=0.70\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.70(1-0.70)}{110}}=0.044](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%3Dp%3D0.70%5C%5C%5C%5C%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%3D%5Csqrt%7B%5Cfrac%7B0.70%281-0.70%29%7D%7B110%7D%7D%3D0.044)
Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:
![P(0.60](https://tex.z-dn.net/?f=P%280.60%3C%5Chat%20p%3C0.80%29%3DP%28%5Cfrac%7B0.60-0.70%7D%7B0.044%7D%3C%5Cfrac%7B%5Chat%20p-%5Cmu_%7B%5Chat%20p%7D%7D%7B%5Csigma_%7B%5Chat%20p%7D%7D%3C%5Cfrac%7B0.80-0.70%7D%7B0.044%7D%29)
![=P(-2.27](https://tex.z-dn.net/?f=%3DP%28-2.27%3CZ%3C2.27%29%5C%5C%5C%5C%3DP%28Z%3C2.27%29-P%28Z%3C-2.27%29%5C%5C%5C%5C%3D0.98840-0.01160%5C%5C%5C%5C%3D0.9768%5C%5C%5C%5C%5Capprox0.9780)
*Use a <em>z</em>-table.
Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.
The correct option is (a).
Answer:
I think it would be 2(8) + 3(5) = x or = 31
Step-by-step explanation:
Answer:
And find it all urself
Step-by-step explanation:
Answer:
3. x = 53
4. x = 60
Step-by-step explanation:
The given angles mean that line QT divides angle PQS.
<em>The measure of </em>
<em> is </em>
<em />
Given that:
![\angle PQS = 3x + 13](https://tex.z-dn.net/?f=%5Cangle%20PQS%20%3D%203x%20%2B%2013)
![\angle SQT = 6x -2](https://tex.z-dn.net/?f=%5Cangle%20SQT%20%3D%206x%20-2)
Since QT divides
;
The equation to calculate
is:
![\angle PQT = \angle PQS - \angle SQT](https://tex.z-dn.net/?f=%5Cangle%20PQT%20%3D%20%5Cangle%20PQS%20-%20%5Cangle%20SQT)
This gives
![\angle PQT = 3x + 13- (6x -2)](https://tex.z-dn.net/?f=%5Cangle%20PQT%20%3D%203x%20%2B%2013-%20%286x%20-2%29)
Open bracket
![\angle PQT = 3x + 13- 6x +2](https://tex.z-dn.net/?f=%5Cangle%20PQT%20%3D%203x%20%2B%2013-%206x%20%2B2)
Collect like terms
![\angle PQT = 13+2- 6x + 3x](https://tex.z-dn.net/?f=%5Cangle%20PQT%20%3D%2013%2B2-%206x%20%2B%203x)
![\angle PQT = 15- 3x](https://tex.z-dn.net/?f=%5Cangle%20PQT%20%3D%2015-%20%203x)
Hence, the measure of
is ![15- 3x](https://tex.z-dn.net/?f=15-%20%203x)
Read more about angles at:
brainly.com/question/13954458