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.
