The volume, $V$ ml, of a high-precision chemical reagent in automated filling bottles is normally distributed such that $\sim N(500, 8^2)$ .

Find the probability that a randomly selected bottle contains more than $512$ ml.

Determine (i) the upper quartile ( $Q_3$ ) of $V$ (ii) the lower quartile ( $Q_1$ ) of $V$

A bottle is defined as an outlier if its volume is greater than $Q3+1.5×(Q3−Q1)Q_3 + 1.5 \times (Q_3 - Q_1)$ or less than $Q1−1.5×(Q3−Q1)Q_1 - 1.5 \times (Q_3 - Q_1)$ .

Calculate the upper and lower volume limits for outliers.

A bottle is selected at random.

Using standardisation, show that the probability that this bottle is not an outlier is $0.993$ to 3 decimal places.

Given that this bottle is not an outlier,

showing your working, find the probability that the volume of reagent in this bottle is less than $488$ ml.

The volume, $V$ ml, of a high-precision chemical reagent in automated filling bottles is normally distributed such that $\sim N(500, 8^2)$ .

Find the probability that a randomly selected bottle contains more than $512$ ml.

Determine (i) the upper quartile ( $Q_3$ ) of $V$ (ii) the lower quartile ( $Q_1$ ) of $V$

A bottle is defined as an outlier if its volume is greater than $Q3+1.5×(Q3−Q1)Q_3 + 1.5 \times (Q_3 - Q_1)$ or less than $Q1−1.5×(Q3−Q1)Q_1 - 1.5 \times (Q_3 - Q_1)$ .

Calculate the upper and lower volume limits for outliers.

A bottle is selected at random.

Using standardisation, show that the probability that this bottle is not an outlier is $0.993$ to 3 decimal places.

Given that this bottle is not an outlier,

showing your working, find the probability that the volume of reagent in this bottle is less than $488$ ml.

2.2 Conditional Probability

Question 11

Markscheme

2.2 Conditional Probability

Question 11

Markscheme

2.2 Conditional Probability

Question 11

2.2 Conditional Probability Questions

2.2 Conditional Probability

Question 11

2.2 Conditional Probability Questions