Answer:
The probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
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:

As the sample size is large, i.e. <em>n</em> = 492 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.
The mean and standard deviation of the sampling distribution of sample proportion are:

Compute the probability that the sample proportion will differ from the population proportion by greater than 0.03 as follows:

![=P(|Z|>2.61)\\\\=1-P(|Z|\leq 2.61)\\\\=1-P(-2.61\leq Z\leq 2.61)\\\\=1-[P(Z\leq 2.61)-P(Z\leq -2.61)]\\\\=1-0.9955+0.0045\\\\=0.0090](https://tex.z-dn.net/?f=%3DP%28%7CZ%7C%3E2.61%29%5C%5C%5C%5C%3D1-P%28%7CZ%7C%5Cleq%202.61%29%5C%5C%5C%5C%3D1-P%28-2.61%5Cleq%20Z%5Cleq%202.61%29%5C%5C%5C%5C%3D1-%5BP%28Z%5Cleq%202.61%29-P%28Z%5Cleq%20-2.61%29%5D%5C%5C%5C%5C%3D1-0.9955%2B0.0045%5C%5C%5C%5C%3D0.0090)
Thus, the probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
Answer:
This is a Categorical variable and the measurement scale is ordinal scale.
Step-by-step explanation:
The measurement scale that is being used to classify sleep is the ordinal measurement. In this question, the variable that is called sleep quality is a categorical variable. categorical variables are variables that have the data representing groups. sleep quality has been given this categorical order extremely low very low low and extreme high.
The ordinal scale is a scale that denotes order it has all variables in a specific order.
In this question, there are 3 conditions that need to be met
1. The number is 3-digit
2. Hundreds digit >7 (number that will fulfill it would be 8 or 9)
3. The tens is 1 more than hundred( since the hundred possibilities is 8 or 9, then 9 in hundreds can't be used since no number higher than 9)
4. The one digit <2( that mean 0, 1)
Using the list above, you can make your possible number:
890
891
Answer:
1. Certain
2. Impossible
3. Likely
4. Unlikely
Step-by-step explanation:
I believe this is correct. Hope this helps!