# Mathematics

Mathematics

1. The phone lines to an airline reservation system are occupied 40% of the time. Assume theevents that the lines are occupied on successive calls are independent. Assume that 10 calls areplaced to the airline. Let Xbe the number of lines that are occupied.

a. What is the name of the probability distribution of X? Obtain the pdf and the cdf tables for thisdistribution.

b. What is the mean of this distribution?

c. What is the standard deviation of this distribution?

2. Suppose a manufacturer of computer chips is experiencing an average of 2% defective chips.

a. If a lot contains 1000 chips, what is the probability that more than 25 chips are defective? HINT. Use the normal approximation to the binomial.

3. An average user of Facebook has 130 friends. We are also given that the standard deviation = 85. This distribution is certainly not normal since it only takes on integer values. Consider a simple random sample of 30 Facebook users.

a. Compute the mean and the standard deviation of the sampling distribution of the mean.Write a sentence describing what this mean signifies.

b. What is the probability that the average number of friends in 30 Facebook users is greaterthan 140? Express your answer in proper notation.

c. Now suppose a simple random sample of 15 users was taken. Describe how your answersto parts (a) and (b) change.