In a performance study of high-altitude inspection drones, the flight duration of the 'AeroScan-X' model is recorded. The duration is found to have a mean of 42.042.042.0 minutes and a standard deviation of 2.52.52.5 minutes.
The flight durations of 95%95\%95% of these drones are observed to fall between 37.037.037.0 minutes and 47.047.047.0 minutes.
Comment on whether a normal distribution may be suitable to model the flight duration of an AeroScan-X drone based on this observation.
Assume that the flight duration of an AeroScan-X drone is indeed modelled by a normal distribution with mean 42.042.042.0 minutes and standard deviation 2.52.52.5 minutes.
(b) (i) Find the probability that the flight duration of a randomly selected drone is exactly 40.040.040.0 minutes.
(b) (ii) Find the probability that the flight duration of a randomly selected drone is between 40.040.040.0 minutes and 45.045.045.0 minutes.
(b) (iii) Two drones are chosen at random. Calculate the probability that both of their flight durations are between 40.040.040.0 minutes and 45.045.045.0 minutes.
The summarised data for the flight durations, ttt minutes, of a random sample of 404040 consumer-grade drones is given below:
∑t=1400and∑(t−tˉ)2=351 \sum t = 1400 \quad \text{and} \quad \sum(t - \bar{t})^2 = 351 ∑t=1400and∑(t−tˉ)2=351Use this data to calculate estimates of the mean and standard deviation of the flight durations of consumer-grade drones.
Using your answers from part (c), compare the flight durations of the industrial 'AeroScan-X' drones and the consumer-grade drones.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.