A data distribution has a mean of 550 and a standard deviation of 100. The distribution is bell shaped. Estimate the data values that define the middle 95% of the data
To estimate the data values that define the middle 95% of the data, we need to find the Z-scores corresponding to the two endpoints of this range.
Since the distribution is bell-shaped and we want to capture 95% of the data, we can use the empirical rule (also known as the 68-95-99.7 rule) for normal distributions.
According to this rule, approximately 95% of the data falls within 2 standard deviations of the mean for a bell-shaped distribution.
So, for the middle 95% of the data:
Lower endpoint = mean - (2 * standard deviation)
Upper endpoint = mean + (2 * standard deviation)
Plugging in the values:
Lower endpoint = 550 - (2 * 100) = 350
Upper endpoint = 550 + (2 * 100) = 750
Therefore, the estimated data values that define the middle 95% of the data are between 350 and 750.