Suppose that 15 of the probability for a certain distributio

Suppose that 15% of the probability for a certain distribution that is N(mu, sigma^2) is below 120 and that 10% is above 250. What are the values of mu and sigma^2?

Solution

Note that

x = u + z*sigma

For the lowest 15%,

z = -1.036433389

Hence,

120 = u - 1.036433389*sigma

For the top 10%,

z = 1.281551566

Hence,

250 = u + 1.281551566*sigma

Hence, solving these two equations,

sigma = 56.08319403

sigma^2 = 3145.324653 [ANSWER]

Also,

u = 178.1264949 [ANSWER]