Long-term telemetry data from an autonomous drone fleet shows that 15% of flight missions result in a high-wind sensor alert. In a random selection of 50 flight missions, let HHH denote the number of missions that triggered a high-wind alert.
Write down a suitable distribution to model HHH.
State one assumption necessary for this model to be valid.
The probability that fewer than kkk missions result in a high-wind alert is less than 0.10.
Find the largest possible value of kkk.
A larger random sample of 200 missions is analyzed.
The probability that at least mmm of these missions result in a high-wind alert is 0.901, correct to 3 decimal places.
Using a suitable approximation, find the value of mmm.
The fleet undergoes a software optimization to better handle wind conditions. Subsequently, a random sample of 25 missions is taken and none of them (0) result in a high-wind sensor alert.
Test, at the 5% level of significance, whether there is evidence that the proportion of missions resulting in high-wind alerts has decreased. State your hypotheses clearly.
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.