The flight duration, LLL minutes, of a specific model of industrial drone follows a normal distribution with mean 54 and standard deviation 6.
A delivery company uses a fleet of 5 drones for a single mission. Find the probability that the total flight duration of these 5 drones exceeds 285 minutes.
The manufacturer wants to establish a "low battery" warning time ttt such that the probability of a drone's flight duration being less than ttt is 0.025. Determine the value of ttt.
To improve efficiency, a lightweight chassis is introduced. A random sample of 40 drones with the new chassis is tested, and their mean flight duration is found to be 56.3 minutes. Assuming the standard deviation remains 6, test, at the 1% level of significance, whether there is evidence that the mean flight duration has increased. State your hypotheses clearly.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.