Cramer's rule:
1 answer:
Answer:
Step-by-step explanation:
To find the value of x, Cramer's rule says you replace the x-coefficients with the equation constants to form the matrix whose determinant is the numerator of the fraction. The denominator is the determinant of the matrix of coefficients. The equation constants are 148 and 246, so you expect to find those in the first column of the numerator (answer choices A and C).
The calculation is carried out correctly only in answer choice A.
You might be interested in
Answer:
There is a 68% chance that between 17% and 30% are smokers.
There is a 95% chance that between 10% and 37% are smokers.
There is a 99.7% chance that between 4% and 44% are smokers.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 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 the sampling distribution of sample proportion is:
The standard deviation of the sampling distribution of sample proportion is:
Given:
<em>n</em> = 40
<em>p</em> = 0.236
Compute the mean and standard deviation of this sampling distribution of sample proportion as follows:
The Empirical Rule states that in a normal distribution with mean <em>µ</em> and standard deviation <em>σ</em>, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be divided into three parts:
- 68% data falls within 1 standard-deviation of the mean.
That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.
- 95% data falls within 2 standard-deviations of the mean.
That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.
- 99.7% data falls within 3 standard-deviations of the mean.
That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.
Compute the range of values that has a probability of 68% as follows:
Thus, there is a 68% chance that between 17% and 30% are smokers.
Compute the range of values that has a probability of 95% as follows:
Thus, there is a 95% chance that between 10% and 37% are smokers.
Compute the range of values that has a probability of 99.7% as follows:
Thus, there is a 99.7% chance that between 4% and 44% are smokers.