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A random sample of size n=285 is taken from a population with a population proportion p=0.71. (You moy find it useful to reference the zatable.) a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion. (Round "expected volue" to 2 decimal plecet and "standord error" to 4 decimal places.) b. What is the probobility that the sampie proportion is between 0.70 and 0.80? (Round " q value to 2 decimal places, and finol enwer to 4 deelmel pleces.) c. What is the probablity that the sampie proportion is less than 0707 (Round " r " value to 2 decimal places, and final anawer to 4 decimal pleces.) Beer botties are filied so that they contain an average of 345mi of beer in each bottie. Suppose that the amount of beer in a botte is notmally distributed with a standard devsation of 8mt. [You may find it useful to reference the ztable.] 0. What is the probabifity that a randoinly selected bocte will have less than 338 mil of beer? (Aound Intermediate calculations to at least 4 decimel places, " zn value to 2 decimal plocet, and flinal antwer to 4 decimat ploces.) b. What is the probsblity that a randomiy selected 6-pack of beet will have a miean aniount lese than 33 ine (Pound Intermediate calculations to at lesst 4 deeimal ptocet, " x " value to 2 decimal pisces, and final antwer to 4 decimal places.) c. What is the proboblity that a fandonty selected 12-pack of beet wili have a mean amourt less than 338 mit (Raund intermediate caiculations to et leate 4 decimal places, " z value to 2 declimal gloces, and final antwer to 4 decimai piocei