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.
