Use relative frequencies obtained from data to determine point estimates of probabilities associated with a discrete random variable.

A quality control inspector randomly selects microchips from a production line and classifies each as defective or non-defective. The results from five different inspectors are shown in the table below. Which sample is expected to provide the best point estimate of the probability that a randomly selected microchip is defective?

A student recorded the number of phone calls received per day over a sample of 200 working days. The results are shown in the table below. Use the data to determine point estimates of the probabilities that on any given working day the office will receive: (a) exactly 2 phone calls [1] (b) fewer than 3 phone calls [1] (c) at least 4 phone calls [1]

A telecommunications company recorded the number of dropped calls during peak hours on 200 separate occasions. The data collected is summarised in the table below. (a) Determine the relative frequency for each number of dropped calls. (b) Use the relative frequencies to estimate the probability that on a randomly selected peak hour, exactly 3 calls will be dropped. (c) Hence, predict the number of occasions out of the next 500 peak hours in which exactly 3 calls will be dropped.

A survey of 180 randomly selected households recorded the number of electric vehicles (EVs) owned by each household. The data is shown in the table below. (a) Use the data to determine the sample proportion of households that own exactly 2 electric vehicles. [1 mark] (b) Determine the point estimate of P(X ≥ 1), where X is the discrete random variable representing the number of electric vehicles owned by a randomly selected household. [1 mark] (c) Calculate the expected number of electric vehicles per household, E(X), using the relative frequencies as point estimates of the probabilities. [2 marks] (d) Use your answer from part (c) to estimate the total number of electric vehicles owned across a suburb of 2400 households, assuming this sample is representative. [1 mark]

A biologist conducts an experiment where a randomly selected seed from a particular plant species is planted, and its germination status (germinated or failed) is recorded. This process is repeated multiple times with different sample sizes. The results from four independent experimental runs are shown in the table below. Which sample would provide the best point estimate of the true probability that a seed from this species will germinate?