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A small independent general...

A small independent general practice has three doctors. Dr Smith sees 40% of the patients, Dr Tran

sees 30% and Dr Jackson sees the rest. Dr Smith requests blood tests on 5% of her patients, Dr Tran

requests blood tests on 8% of his patients and Dr Jackson requests blood tests on 6% of her patients.

An auditor from the Australian Health Insurance Commission randomly selects a patient from the

past week;

a) What is the probability that the selected patient had a blood test as a result of a visit to the

general practice?

b) What is the probability that given the selected patient had a blood test as a result of a visit to

the general practice; they were seen by Dr Smith?

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The lifetime of a certain brand of light bulb is normally distributed, with a mean of 7500 hours and

a standard deviation of 700 hours.

a) If the light bulbs carry a warranty for 6000 hours, what proportion of the bulbs will fail before

the warranty expires?

b) The manufacturer replaces for free all bulbs that fail while under warranty. If they are willing

to replace 2% of light bulbs that fail, what warranty should they offer?

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