(i) To find the probability that an apple is graded as medium, we need to calculate the probability that its weight is between 90 and 140 grams. We standardize these values using the formula:

\(z = \frac{x - \mu}{\sigma}\)

For 90 grams: \(z_1 = \frac{90 - 120}{24} = -\frac{5}{4}\)

For 140 grams: \(z_2 = \frac{140 - 120}{24} = \frac{5}{6}\)

The probability that an apple is graded as medium is:

\(\Phi\left(\frac{5}{6}\right) - \Phi\left(-\frac{5}{4}\right)\)

Using standard normal distribution tables or a calculator, we find:

\(\Phi(0.8333) - (1 - \Phi(1.25)) = 0.7975 - 0.1056 = 0.6919\)

Rounding to 3 significant figures gives 0.692.

(ii) We use the binomial distribution to find the probability that at least two apples are graded as medium. Let \(X\) be the number of medium apples out of 4, where \(X \sim \text{Binomial}(4, 0.692)\).

We need \(P(X \geq 2) = 1 - P(X = 0) - P(X = 1)\).

\(P(X = 0) = (1 - 0.692)^4\)

\(P(X = 1) = 4 \times 0.692^1 \times (1 - 0.692)^3\)

Calculating these:

\(P(X = 0) = 0.00899\)

\(P(X = 1) = 0.0808757\)

Thus, \(P(X \geq 2) = 1 - 0.00899 - 0.0808757 = 0.910\).