Find the variance if X~N(0.02) and 95% of the data lies between -7 and 7.
To find the variance for a normal distribution, we need to know the standard deviation. In this case, we are given that 95% of the data lies between -7 and 7, which implies that these values are approximately 1.96 standard deviations away from the mean (since 95% of the data falls within approximately two standard deviations from the mean in a normal distribution).
We can use this information to set up an equation to solve for the standard deviation:
7 = 1.96 * standard deviation
Solving for the standard deviation:
standard deviation = 7 / 1.96
Now that we have the standard deviation, we can square it to find the variance:
Variance = (standard deviation)^2
Variance = (7 / 1.96)^2
To calculate the exact value, we can use a calculator or a computer program:
Variance ≈ 25.24
Therefore, the variance is approximately 25.24 for X~N(0.02), where 95% of the data lies between -7 and 7.