According to the ABS, the average length of stay by tourists in Queensland’s hotels, motels and serviced apartments is 2.2 days with a standard deviation of 1.2 days. A sample of 65 randomly selected tourists is taken.

(a) What is the probability that the average length of stay for the 65 chosen in the sample is less than 2.2 days?

(b) What is the probability that the average length of stay for the 65 chosen in the sample is between 2.1 and 2.4 days?

(c) What is the probability that the average length of stay for the 65 chosen in the sample is between2.4 and 3 days?

(d) What is the minimum value for the average length of stay, for the chosen sample of 65, for the 5% of tourists who stay longest?