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Answer:
Step-by-step explanation:
From the given options we find that
SAT scores of high school senios can be expected to be normal
IIoption cannot be correct as this salaries would be higher than average and need not be bell shaped so nor notmal
III Option show sizes of 17 year old mates can be expected to be normal
IV option is also normal since the age at which a child loses his or her teeth would have population of large size with mean and symmetrical distribution
IV option is incorrect as between 1 and 6 is a certain event with p = 1
The situations expected to be approximately normally distributed are
- Option A: The SAT scores of high school seniors
- Option C: The shoe sizes of 17-year old males
- Option D: The age at which a child looses his or her first tooth
How to find if the situation can be approximated by normal distribution?
A random variable pertaining normal distribution is always tracking an effect which averages to some single quantity and varies less and less from that single quantity.
This is like, that random variable is tracking some "force" which is itself alone affecting the system in consideration. That force, due to environmental disturbances, get deviated from its mean, and the effect of those environmental disturbance averages to zero and is almost zero if the force is deviated from its average.
The graph of values of a normally distributed random variable is bell shaped.
Using the above fact, we have:
- Case 1: -the SAT scores of high school seniors
In this, the scoring is done by humans(and in large enough quantity). All humans average to certain IQ and education (as education of them is common which is high school and age too). So they will average to single number and other scores will lie above or below that average score.
So yes, this can be approximated by normal distribution.
- Case 2: -the salaries for members of a professional football team
Some players might be getting super high salaries due to their fame and demand, and some might be newcomers so might not be getting much pay. Also, since a football team is not much large, thus, the distribution might be oddly biased and not bell shaped. Thus, this cannot be approximated by normal distribution.
- Case 3: -the shoe sizes of 17-year-old males
The age is specified same, and gender too. What can vary? Foot size. This averages to constant as height of 17 year old males will get to some constant and doesn't vary much for a large population. Since all 17 year males are considered, so a large enough population is considered, thus, giving a good above and below average height pertaining values.
So the graph will be bell shaped and thus, this case can be approximated by normal distribution.
- Case 4: -the age at which a child loses his or her first tooth
This also, can come to an average single age and other ages recorded will lie close to that average both above and below. Thus, the graph will be bell shaped and thus, this case can be approximated by normal distribution.
- Case 5: -the probability of rolling a given number between 1 and 6 on a number cube
The probability of a single given number on a six faced die is 1/6. It doesn't change. The "probability" already covered those environmental variation, thus, giving only a constant value 1/6.
Thus, it is uniform value and cannot be modeled by normal distribution.
Thus,
The situations out of the given options which can be expected to be approximately normally distributed are
- Option A: The SAT scores of high school seniors
- Option C: The shoe sizes of 17-year old males
- Option D: The age at which a child looses his or her first tooth
Learn more about normal distributions here:
https://brainly.com/question/15395456
