Answer:
The distance between the points is approximately 6.4
Step-by-step explanation:
The given coordinates of the points are;
(2, -2), and (6, 3)
The distance between two points, 'A', and 'B', on the coordinate plane given their coordinates, (x₁, y₁), and (x₂, y₂) can be found using following formula;
Substituting the known 'x', and 'y', values for the coordinates of the points, we have;
Therefore, the distance between the points, (2, -2), and (6, 3) = √(41) ≈ 6.4.
Answer:
68% of the rates are expected to be betwen 0.718 and 0.762
95% of the rates are expected to be betwen 0.696 and 0.784
99.7% of the rates are expected to be betwen 0.674 and 0.806
Step-by-step explanation:
Check for conditions
For this case in order to use the normal distribution for this case or the 68-95-99.7% rule we need to satisfy 3 conditions:
a) Independence : we assume that the random sample of 400 students each student is independent from the other.
b) 10% condition: We assume that the sample size on this case 400 is less than 10% of the real population size.
c) np= 400*0.74= 296>10
n(1-p) = 400*(1-0.74)=104>10
So then we have all the conditions satisfied.
Solution to the problem
For this case we know that the distribution for the population proportion is given by:
So then:
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
68% of the rates are expected to be betwen 0.718 and 0.762
95% of the rates are expected to be betwen 0.696 and 0.784
99.7% of the rates are expected to be betwen 0.674 and 0.806