7.5 Repeated Sampling

One way of getting more accurate results with respect to the population when sampling is to conduct multiple samples.

Each sample will have a mean and a standard deviation. The means will form a normal distribution on their own with the mean being equal to the population mean.

The notation is for 'the average of the sample means'

The distribution of the sample means will have a standard deviation

The notation is for the 'the standard deviation of the sample means'

Ex 1 The tires on a rental car fleet have lifetimes that are normally distributed with a mean life of 64 000 km and a standard deviation of 4800 km. Every week a mechanic checks the tires on ten randomly selected cars.

(a) What are the mean and standard deviation of these samples?

(b) How likely is the mechanic to find a sample mean of 62500 km or less?

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