Suppose x is a random variable with mean and standard deviation. If a large number of trials is observed, at least what percentage of these values is expected to lie beween mean-2(standard deviation) and mean + 2(standard deviation)
could someone help me i'm so lost? thank you sooooo much!!!
Memorize it. Two standard deviations contain 95 percent of the population.
Of course, I'm here to help! To determine the percentage of values expected to lie between mean-2(standard deviation) and mean + 2(standard deviation), we can use the empirical rule, also known as the 68-95-99.7 rule.
According to this rule, for any distribution that is approximately bell-shaped (following a normal distribution):
- Approximately 68% of the values will fall within 1 standard deviation of the mean.
- Approximately 95% of the values will fall within 2 standard deviations of the mean.
- Approximately 99.7% of the values will fall within 3 standard deviations of the mean.
In this case, since we are interested in the range between mean-2(standard deviation) and mean+2(standard deviation), we are looking for the percentage of values falling within 2 standard deviations of the mean.
Given that a large number of trials are observed, we can assume that the distribution approaches a normal distribution. Hence, approximately 95% of the values can be expected to lie between mean-2(standard deviation) and mean+2(standard deviation).
So, to answer your question, at least 95% of the values are expected to lie between mean-2(standard deviation) and mean+2(standard deviation).