Let D = {x| x is a student} be the domain, and let ƒ(x) = “date of birth” be the possible function. Determine if the relation is
1 answer:
Remember that a function is a special type of relation in which each element of the domain is paired with only one element in the range; in other words for each 
value, there is only a 
value.
Since D = {x| x is a student}, the domain of the relation is the set of all students; on the other hand, <span>ƒ(x) = “date of birth”, so the range of the relation is the set of the birth dates of the students. Since in a room of 23 people there is a 50% chance of two people sharing the same date of birth, it is inevitable that in the set of all the students there is at least two students that share the same date of bird; therefore two elements in the domain will be paired with the same element in the range. Given that, We can conclude that the relation is not a function.
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Since D = {x| x is a student}, the domain of the relation is the set of all students; on the other hand, <span>ƒ(x) = “date of birth”, so the range of the relation is the set of the birth dates of the students. Since in a room of 23 people there is a 50% chance of two people sharing the same date of birth, it is inevitable that in the set of all the students there is at least two students that share the same date of bird; therefore two elements in the domain will be paired with the same element in the range. Given that, We can conclude that the relation is not a function.
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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