Mathematical Methods · Unit 4 · Continuous random variables and the normal distribution · General continuous random variables
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A quality control engineer monitors the setting time (in hours) of a new concrete mix. A random sample of 80 batches was tested, and the setting times were recorded. The data are summarised in the table below. A batch is selected at random from this sample. Determine the probability that the setting time is: (a) between 3 and 5 hours (b) at least 5 hours (c) less than 4 hours or at least 6 hours.
A shipping company records the loading time (in minutes) for 200 containers at a port facility. The data is summarised in the table below. (a) Use the data to estimate the probability that a randomly selected container has a loading time less than 30 minutes. **(2 marks)** (b) Estimate the probability that a randomly selected container has a loading time between 25 and 45 minutes, assuming loading times are uniformly distributed within each interval. **(3 marks)**
The relative frequency histogram below displays the daily electricity consumption (in kilowatt-hours) for a sample of 500 households over one year. Determine the probability that a randomly selected household from this population consumes between 15 and 25 kilowatt-hours per day.
A research team collected data on the waiting times (in minutes) for customers at a service centre over a one-week period. The table below shows the relative frequency distribution for waiting times. (a) Use the relative frequency distribution to estimate the probability that a randomly selected customer waits between 8 and 18 minutes. (3 marks) (b) Determine the median waiting time for customers, correct to one decimal place. (1 mark)