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Answer :
Using the Empirical Rule, it is found that the percentages are given as follows:
a) 68%.
b) 47.5%.
c) 97.5%.
What does the Empirical Rule state?
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.
Item a:
Both within 1 standard deviation of the mean, hence 68%.
Item b:
Between the mean and two standard deviations above the mean, hence 95% of 50%(as the normal distribution is symmetric), hence:
P = 95% x 0.5 = 47.5%.
Item c:
Two standard deviations below the mean and below, hence only the bottom 5/2 = 2.5% is removed, so 97.5%.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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