2019 July

Suppose ABC restaurant delivers one special type of pizza, which is sold for $10.

This pizza costs the restaurant $6 to make. The restaurant has the following policy

regarding their delivery service: if the pizza takes longer than half an hour to

arrive, there is no charge. Let the random variable X denotes the restaurant's profit

for any one pizza. Past historical records showed that delivery that took longer

than half an hour happened only 10% of the time.

Apply the concepts of random variables and compute the mean profit per

pizza.

(ii) If ABC restaurant wants to increase its mean profit per pizza to $3.90,

analyse and explain how much should it raise the price from $10.

The probability that a person has a certain disease is 0.03. Medical diagnostic

tests are available to determine whether the person actually has the disease. If the

disease is actually present, the probability that the medical diagnostic test will

give a positive result (indicating that the disease is present) is 0.90. If the disease

is not actually present, the probability of a positive test result (indicating that the

disease is present) is 0.02. Suppose that the medical diagnostic test has given a

positive result (indicating that the disease is present).

Analyse and compute the probability that the disease is actually present.

Analyse and compute the probability of a positive test result.