A business man must travel to five different destinations each year. He takes three flights to reach each of these destinations. Suppose that the first flight is on time 43% of the time, the second flight is on time 14.9% of the time and the third flight is on time 42% of the time. Also suppose the flight arrivals are independent.
(a) Let X be the number of times the first flight is on time for his five trips during the year. The mean and variance of X are, respectively, ___ and ___.
(b) What is the probability that the business man's second flight is on time for exactly three of his trips during the year? ____
(c) What is the probability that the business man's third flight is on time for at least two of his trips during the year? ____
(d) In two years, what is the probablity that the business man's first flight is on time exactly five times? ____
Daily water intake (including water used in drinks such as coffee, tea and juice) for Canadian adults follows a normal distribution with mean 1.8 litres and standard deviation 0.32 litres.
(e) Can you calculate the probability that the mean daily water intake for a random sample of two Canadian adults is less than 1.59 litres? If you can, enter the probability in the answer box. If you can't, type the word No. _____
(f) What is the probability that the mean daily water intake for a random sample of 35 Canadian adults is greater than 1.74 litres? ____
(g) What is the probability that the total daily water intake for a random sample of 44 Canadian adults is between 74.42 and 81.13 litres? ____
(h) Using the 68-95-99.7 Rule, approximately 95% of samples of 25 Canadian adults will have mean daily water intakes between _____ and _____.
(i) If we take a random sample of 18 Canadian adults, there is an 11% chance that their mean daily water intake will be greater than _____
Business analysts estimate the length of time people work in the same job follows some right-skewed distributon with a mean of 6.39 years and a standard deviation of 4.55 years.
(j) Can you calculate the probability that the average time two people have worked in the same job is less than 6.12 years? If you can, enter the probability in the answer box. If you can't, type the word No. ______
(k) What is the probabillity that the mean amount of time a random sample of 33 people have worked at the same job is between 5.09 and 7.09 years? _____
(l) What is the probability that the total time people work at the same job for a random sample of 44 people exceed 315.26 years? _____
(m) What is the probability that the mean time people work at the same job for a random sample of 56 people is exactly 7.07 years? _____
Are your answers for questions (f), (g), (k) and (l) exact or approximate? Explain.