Lieutenant Columbo is a shrewd and persistent detective work…

Lieutenant Columbo is a shrewd and persistent detective working homicides for LAPD. Along with his unassuming manner, rumpled raincoat, and penchant for quoting his beloved wife, on of Columbo’s most distinctive features is the constant supply of cigars he seems to have. During a shift Columbo goes through an average of 8.471 cigars. What is the probability Columbo goes through two to four cigars, inclusive, during the first half of his shift? Round your answer to the third decimal place.