Answer:
a) (1215, 1297)
b) (1174, 1338)
c) (1133, 1379)
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 1256
Standard Deviation, σ = 41
Empirical Rule:
- Also known as 68-95-99.7 rule.
- It states that almost all the data lies within three standard deviation for a normal data.
- About 68% of data lies within 1 standard deviation of mean.
- About 95% of data lies within two standard deviation of mean.
- About 99.7% of data lies within 3 standard deviation of mean.
a) range of years centered about the mean in which about 68% of the data lies
68% of data will be found between 1215 years and 1297 years.
b) range of years centered about the mean in which about 95% of the data lies
95% of data will be found between 1174 years and 1338 years.
c) range of years centered about the mean in which about all of the data lies
All of data will be found between 1133 years and 1379 years.
Range is set of all y-values. To find a range of graphed function, we need to know that range starts from the minimum value of graph to maximum value. That's because the minimum value is the least value that you can get by substituting the domain and the maximum value is the largest value that you can get by substituting the domain as well.
Now we don't talk about domain here, we talk about range. See the attachment! You are supposed to focus on y-axis, plane or vertical line. See how the minimum value of function is the negative value while the maximum value is positive.
That means any ranges that don't contain the negative values are cleared out. (Hence A and C choices are wrong.)
Next, range being set of all real numbers mean that graphed functions don't have maximum value or minimum value (We can say that both max and min are infinite.)
Take a look at line graph as an example of range being set of all real numbers, or cubic function.
Answer/Conclusion
- The range exists from negative value which is -9 to the maximum value which is 5.
- That means the range is -9<=y<=5
