The yield of a specific chemical reaction, $Y$ grams, is modeled by a normal distribution such that $\sim \text{N}(120, 15^2)$ .

Determine the probability that a randomly selected batch results in a yield of less than 138 g.

Calculate the upper quartile, $Q_3$ , of the yield $Y$ .

Using the symmetry of the distribution, write down the lower quartile, $Q_1$ , of $Y$ .

An outlier in this process is defined as any yield $Y$ such that $Y < h$ or $Y > k$ , where

Q_1 - 1.5 \times (Q_3 - Q_1) \quad \text{and} \quad k = Q_3 + 1.5 \times (Q_3 - Q_1)

Calculate the value of $h$ and the value of $k$ .

Find the probability that a randomly selected batch yield is classified as an outlier.

The yield of a specific chemical reaction, $Y$ grams, is modeled by a normal distribution such that $\sim \text{N}(120, 15^2)$ .

Determine the probability that a randomly selected batch results in a yield of less than 138 g.

Calculate the upper quartile, $Q_3$ , of the yield $Y$ .

Using the symmetry of the distribution, write down the lower quartile, $Q_1$ , of $Y$ .

An outlier in this process is defined as any yield $Y$ such that $Y < h$ or $Y > k$ , where

Q_1 - 1.5 \times (Q_3 - Q_1) \quad \text{and} \quad k = Q_3 + 1.5 \times (Q_3 - Q_1)

Calculate the value of $h$ and the value of $k$ .

Find the probability that a randomly selected batch yield is classified as an outlier.

4.5.1 Statistical distributions (A-level only)

4.5.1 Statistical distributions (A-level only) Questions