15. Incorrect. The answer is true, not false.

The probability the mineral economist is interesting is P [23 < X < 43]. Subtracting the mean, we get:

P [23 - 33 < X - 33 < 43 - 33] = P [-10 < X - 33 < 10] = P [ |X - μ | < 10 ] .

We can apply the Chebyshev's theorem to calculate the minimum probability. Observe that 10 = kσ, where σ = standard deviation of X and k is constant. Because the variance of X is 16, its standard deviation is 4. So, k = 5/2. Applying the Chevyshev's inequality:

P [23 < X < 43] = P [ |X - μ | < (5/2)*4 ] ≥ 1 - 1 / (5/2)^0.5

P [23 < X < 43] ≥ 21/25