Answer:
The probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
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:
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)
The information provided is:
![p=0.22\\n=276](https://tex.z-dn.net/?f=p%3D0.22%5C%5Cn%3D276)
As the sample size is large, i.e. <em>n</em> = 276 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion.
Compute the value of
as follows:
![P(\hat p-p](https://tex.z-dn.net/?f=P%28%5Chat%20p-p%3C0.06%29%3DP%28%5Cfrac%7B%5Chat%20p-p%7D%7B%5Csigma_%7B%5Chat%20p%7D%7D%3C%5Cfrac%7B0.06%7D%7B%5Csqrt%7B%5Cfrac%7B0.22%281-0.22%29%7D%7B276%7D%7D%7D%29%5C%5C%5C%5C%3DP%28Z%3C2.41%29%5C%5C%5C%5C%3D0.99202%5C%5C%5C%5C%5Capprox%200.992)
Thus, the probability that the sample proportion will differ from the population proportion by less than 6% is 0.992.
Answer:
B
Step-by-step explanation:
The vertex is the turning point of the quadratic function.
In this case it lies on the x- axis at (2, 0 ) → B
Area = Length * Width
Area = 6 * 1/12 = 1/2
Area = 1/2 = 0.5
Area = 0.5 inches²
Hope this explains it.
Answer: The outcome of spinning a spinner with five equal outcomes
Step-by-step explanation: