In a factory, billions nails are produced each week. The quality control group found that about 0.25% of the nails are defective A) In a box of 2000 nails, what is the probability that exactly 3 nails are defective? B) Use Poisson distribution to approximate the answer to part (a).

The number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page.    What is the probability that the typist makes 3 errors on a page?  What is the probability that a randomly selected page does not need to be retyped?

Can I get help for question B?

According to a survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five. a.  What is the probability of receiving no e-mails during an hour (to 4 decimals)?   b.  What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.   c.  What is the expected number of e-mails received during minutes (to 2 decimals)?   d.  What is the probability that no e-mails are received during minutes (to 4 decimals)?