## SpeedWay airline flies from city A to city B. The flight time is normally distributed with a mean of 260 minutes and a standard deviation of 15 minutes.

A flight is late if it takes longer than 275 minutes.

(a) [2 marks] Calculate the probability that a flight is not late.

(b) [3 marks] The flight is considered on time if it takes between m and 275 minutes. The probability that a flight is on time is 0.830. Find the value of m.

(c) [3 marks] During a week, SpeedWay has 12 flights from city A to city B. The time taken for any flight is independent of the time taken by any other flight. Calculate the probability that at least 7 of these flights are on time.

(d) [4 marks] Given that at least 7 of these flights are on time, find the probability that exactly 10 flights are on time.

(e) [3 marks] SpeedWay increases the number of flights from city A to city B to 20 flights each week, and improves their efficiency so that more flights are on time. The probability that at least 19 flights are on time is 0.788.A flight is chosen at random. Calculate the probability that is is on time.

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