Respuesta :
Using the Empirical Rule, it is found that:
a) 95% of students have scores between 70 and 130.
b) 83.85% of students have scores between 55 and 115.
c) 99.7% of scores will fall between 55 and 145.
What is the Empirical Rule?
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Also, it is important to note that the normal distribution is symmetric, that is, 50% of the measures are below the mean and 50% are above.
Item a:
Within two standard deviations of the mean, hence, 95% of students have scores between 70 and 130.
Item b:
Within 3 below and 1 above, hence, considering the symmetry of the normal distribution:
0.997 x 50 + 0.68 x 50 = 83.85
83.85% of students have scores between 55 and 115.
Item c:
99.7% of scores fall within 3 standard deviations of the mean, hence:
100 - 3 x 15 = 55
100 + 3 x 15 = 145.
99.7% of scores will fall between 55 and 145.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
