Question

Question 2

Suppose the waiting time of a bus follows a uniform distribution on [0, 20]. (a) Find the probability that a passenger has to wait for at least 12 minutes. (b) Find the mean and interquantile range of the waiting time.

Question 3
Each year, a large warehouse uses thousands of fluorescent light bulbs that are burning 24 hours per day until they burn out and are replaced. The lifetime of the bulbs, X, is a normally distributed random variable with mean 620 hours and standard deviation 20 hours.

1. (a) If a light bulb is randomly selected, how likely its lifetime is less than 582 hours?

2. (b) The warehouse manager orders a shipment of 500 light bulbs each month. How

   many of the 500 bulbs are expected to have a lifetime that is less than 582 hours?

3. (c) The supplier of the light bulbs and the manager agree that any bulb whose lifetime

   is among the lowest 1% of all possible lifetimes will be replaced at no charge. What is the maximum lifetime a bulb can have and still be among the lowest 1% of all lifetimes?

Question 4
60% of students go to HKUST by bus. There are 10 students in the classroom. (a) What is the probability that exactly 5 of the students in the classroom go to

HKUST by bus?
(b) What is the mean number of students going to HKUST by bus?

Question 5
Peter is tossing an unfair coin that the probability of getting Head is 0.75. Let X be the random variable of number of trails that Peter get the first Head.
(a) Find the probability that the number of trails is five.
(b) Find the mean and standard deviation of random variable, X.

Question 6

Given that the population proportion is 0.6, a sample of size 1200 is drawn from the population.

1. (a) Find the mean and variance of the sampling distribution of sample proportion.

2. (b) Find the probability that the sample proportion is less than 0.58.

3. (c) If the probability that the sample proportion is greater than k is 0.6, find the value of k.

Answer 1