1.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 14.6% 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,
(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?
2. Daily water intake (including water used in drinks such as coffee, tea and juice) for Canadian adults follows a normal distribution with mean 1.35 litres and standard deviation 0.33 litres.
(a) What is the probability that the total daily water intake for a random sample of 49 Canadian adults is between 62.34 and 68 litres?
(b) If we take a random sample of 13 Canadian adults, there is an 11% chance that their mean daily water intake will be greater than
c) are your answers for part a, exact or approximate. explain.
3. Business analysts estimate the length of time people work in the same job follows some right-skewed distributon with a mean of 6.42 years and a standard deviation of 4.7 years.
(a) Can you calculate the probability that the average time two people have worked in the same job is less than 6.15 years? If you can, enter the probability in the answer box. If you can't, type the word No.
(b) What is the probabillity that the mean amount of time a random sample of 31 people have worked at the same job is between 5.01 and 6.78 years?
(c) What is the probability that the total time people work at the same job for a random sample of 47 people exceed 351.36 years?
(d) What is the probability that the mean time people work at the same job for a random sample of 58 people is exactly 7.1 years?
4. A large shipment of Granny Smith apples arrives at a grocery store. Weights of the apples are known to follow a normal distribution with mean 149 grams and standard deviation 12 grams.
(a) You select a sample of 3 apples. Can you calculate the probability that the mean weight of the apples in the sample is less than 147.82? If you can, enter the probability in the answer box. If you can't, type the word No.
(b) If you select a random sample of 40 apples, what is the probability that the mean weight of the apples in the sample is between 147.25 and 153.52?
(c) If you select a random sample of 50 apples, what is the probability that the total weight of the apples is greater than 7470.36 grams?