The operational lifespan, LLL hours, of a specific high-performance drone motor is modelled by a normal distribution such that L∼N(150,122)L \sim N(150, 12^2)L∼N(150,122).
Determine the probability that a motor chosen at random has a lifespan exceeding 175175175 hours.
Calculate (i) the upper quartile (Q3Q_3Q3) of LLL (ii) the lower quartile (Q1Q_1Q1) of LLL
A motor's lifespan is classified as an outlier if it is greater than Q3+1.5×(Q3−Q1)Q_3 + 1.5 \times (Q_3 - Q_1)Q3+1.5×(Q3−Q1) or smaller than Q1−1.5×(Q3−Q1)Q_1 - 1.5 \times (Q_3 - Q_1)Q1−1.5×(Q3−Q1).
Find the lower and upper limits for outliers for these drone motors.
A drone motor is selected for testing.
By standardising the limits found in part (c), show that the probability that this motor is not an outlier is 0.9930.9930.993 to 3 decimal places.
Given that the motor's lifespan is not an outlier,
showing your working, determine the probability that the motor lasts less than 140140140 hours.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.