Find the variance if X~N(0.02) and 95% of the data lies between -7 and 7.
To find the variance, we need to know the mean of the normal distribution. In this case, the mean is not given directly, but we have some information about the data.
Given that 95% of the data lies between -7 and 7, we can infer that these values represent the 2 standard deviations (2σ) from the mean in a normal distribution. Since 95% of the data falls within this range, we can use the empirical rule to determine that the standard deviation (σ) is equal to half of the range between the upper and lower bounds, divided by 2.
So, the standard deviation (σ) can be calculated as:
σ = (7 - (-7)) / 4
σ = 14 / 4
σ = 3.5
Now that we have the standard deviation, we can calculate the variance (σ^2) by squaring the standard deviation:
Variance (σ^2) = (3.5)^2
Variance ≈ 12.25
Therefore, the variance of the normal distribution is approximately 12.25.