The network monitoring company Cyber Techs has reported that 90% of e-mails are spam. (Hint: Either an e-mail is spam or not spam!)

a.What are the mean and standard deviation of the number of real message you should expect to find in your inbox if your inbox contains 30 messages?

b.What is the probability that you'll find only 1 or 2 real message if your inbox contains 30 messages?

Bonus Questions (Optional)

c.Recently, you installed a spam filter. You observe that over the past week it okayed only 141 of 1420 e-mails you received, classifying the rest as junk (i.e. spam). Should you be worry that the filtering is too aggressive? Find the probability that no more than 141 of 1420 e-mails is a real message?