Question Type 2: Finding the interval for which a specific percentage of data is concentrated Exercises

A distribution has mean $\mu = 50$ and is approximately normal. If 68% of data lies between 45 and 55, find the variance.

Assuming a normal distribution with mean $\mu = 100$ and variance $\sigma^2 = 16$, estimate the percentage of data that lies between 92 and 108.

Assuming a normal distribution with mean $\mu = 8$, 95% of data falls between 6.5 and 9.5. Calculate the variance.