Q1

Uber fares in a metropolitan city are known to follow a normal distribution with an average fare of $25.00 and a standard deviation of $3.00.

(a) What is the probability that a randomly selected uber fare exceeds $30.00?

(b) If an uber driver on a morning shift had 20 customers, what is the probability that the average fare per trip during the shift was less than $24.50?

(c) If an uber driver had 25 customers during a shift, what is the probability that the total fare during the shift exceeds $650?

Question 2

(a) A shop in downtown Perth is considering moving from its present location to Freemantle. One factor in this decision is the amount of time the shop's employees spend travelling to work. A random sample of 18 employees reveals that the mean and standard deviation of the time required to get to work are 37.5 and 11.3 minutes, respectively. Estimate the 95% confidence interval of the mean time to get to work. State all your assumptions and interpret your result.

(b) One factor in choosing a location for a new clothing store is the mean clothing expenditure per household in the surrounding area. A survey of 16 households reveals that the mean and standard deviation of annual expenditure on clothes is $420 and $90, respectively. Can we conclude at the 5% level that the population mean annual expenditure is less than $500? State any assumptions necessary, conduct this test and interpret your result.