Question 2

Suppose the waiting time of a bus follows a uniform distributionon [0, 20]. (a) Find the probability that a passenger has to waitfor at least 12 minutes. (b) Find the mean and interquantile rangeof the waiting time.

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

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

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

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

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

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

Question 4
60% of students go to HKUST by bus. There are 10 students in theclassroom. (a) What is the probability that exactly 5 of thestudents 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 gettingHead is 0.75. Let X be the random variable of number of trails thatPeter 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 size1200 is drawn from the population.

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

2. (b) Find the probability that the sample proportion is less than0.58.

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