The volume, VVV ml, of a high-precision chemical reagent in automated filling bottles is normally distributed such that V∼N(500,82)V \sim N(500, 8^2)V∼N(500,82).
Find the probability that a randomly selected bottle contains more than 512512512 ml.
Determine (i) the upper quartile (Q3Q_3Q3) of VVV (ii) the lower quartile (Q1Q_1Q1) of VVV
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)Q3+1.5×(Q3−Q1) or less than Q1−1.5×(Q3−Q1)Q_1 - 1.5 \times (Q_3 - Q_1)Q1−1.5×(Q3−Q1).
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 0.9930.9930.993 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 488488488 ml.
330 exam-style questions on Edexcel A Level Maths Conditional Probability, covering 2.1 Set Notation, 2.2 Conditional Probability, 2.3 Conditional Probabilities in Venn Diagrams, 2.4 Probability Formulae, and 2.5 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.