17. Correct. The answer is false. We know that X ~ N(7,4). An important theorem that relates the normal and the Chi-square distribution functions establishes that the square of a standardized random variable, which follows a normal distribution with mean zero and standard deviation one, has a Chi-square distribution function with one a degree of freedom.

Z ~ N(0,1) and Z² ~ χ²(1)

If X ~ N(7,4), then the random variable Y = (X-7)²/4 ~ χ²(1). Therefore:

P[15 ≤ (X-7)² ≤ 20] = P[15/4 ≤ (X-7)²/4 < 20/4] = P[3.75 ≤ Y < 5] = P[Y ≤ 5] - P[Y ≤ 3.75]

Using the Chi-square distribution table, we have that:

P[Y ≤ 5] - P[Y ≤ 3.75] = 0.9746 - 0.9472 ≈ 2.75%