1.According to Internet security experts, approximately 90% of all e-mail messages are spam (unsolicited commercial e-mail), while the remaining 10% are legitimate. A system administrator wishes to see if the same percentages hold true for the email traffic on her servers. She randomly selects e-mail messages and checks to see whether or not each one is legitimate. (Unless otherwise specified, round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.)

Assuming that 90% of the messages on these servers are also spam, compute the probability that the first legitimate e-mail she finds is the third message she checks.________

Compute the probability that the first legitimate e-mail she finds is the third or fourth message she checks.______

Compute the probability that the first legitimate e-mail she finds is among the first three messages she checks_______

On average, how many messages should she expect to check before she finds a legitimate e-mail? (Round your answer to one decimal place.)______ messages

2.A normal distribution has a mean of 69 and a standard deviation of 4. Use the standard normal table to find the indicated probability for a randomly selected x-value from the distribution. Round all probabilities to 5 decimal places.

Find the z score for 66______

P(x66)=_____

Find the z score for 76_____

P(x76)____

P(66x76)______

3.Air-USA has a policy of booking as many as 26 persons on an airplane that can seat only 25. (Past studies have revealed that only 83% of the booked passengers actually arrive for the flight.)

Find the probability that if Air-USA books 26 persons, not enough seats will be available.

prob =_____

Is this probability low enough so that overbooking is not a real concern for passengers if you define unusual as 5% or less?

• yes, it is low enough not to be a concern
• no, it is not low enough to not be a concern

What about defining unusual as 10% or less?

• no, it is not low enough to not be a concern
• yes, it is low enough not to be a concern