Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
<h3>What does the Empirical Rule state?</h3>
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.
Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.
140 = 110 + 2 x 15.
These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
This sequence (1.6, 0.8, 0.4, 0.2,... ) is geometric. We have formula for any member of geometric sequence: If a1=1.6 then:The solution for all these equations is: q=0.5. We have: a1=1.6, q=0.5 and this is geometric sequence.
If a1=1.6 then:
The solution for all these equations is: q=0.5. We have: a1=1.6, q=0.5 and this is geometric sequence.