QUESTION 2 (25)
2.1. A small town is served by three airline companies, X, Y and Z. From airport records, it is known that 45% of flights are provided by X, 35% of flights are provided by Y, while the remaining flights are provided by Z. History has shown that flights provided by X are delayed 15% of the time, flights provided by Y are delayed 10% of the time while flights provided by Z are delayed 8% of the time. A flight has just been delayed.
Calculate the probability that it was provided by Y. (7)
2.2. The life span of an imported brand of kettles sold by an appliance giant is normally distributed with a mean of 96 months and a standard deviation of 12 months.
2.2.1. What percentage of these kettles will last between 90 and 110 months? (5)
2.2.2. The appliance giant offers a replacement guarantee on kettles which malfunction within a certain time of the purchase, but due to financial constraints, can only afford a maximum of 5% replacements. What must the guarantee period be? (6)
2.3. Statistics show that only 25% of taxpayers submit their tax return before the deadline date.
For a sample of six adults, what is the probability that at least two have submitted their tax returns before the deadline date.
