Suppose packages of cream cheese, coming from an automated processor, have weights that are normally distributed. For one day’s production run, the mean is 8.2 ounces and standard deviation is 0.1 ounce.
(a) If the packages of cream cheese are labeled 8 ounces, what proportion of the packages weigh less than the labeled amount?
(b) If a package of cream cheese is selected at random, what is the probability that this package weighs greater than 8.26 ounces?
(c) If only 5% of the packages exceed a specified weight w, what is the value of w?
(d) Suppose 4 packages are selected at random from the day’s production. What is the probability that the average weight of the four packages is greater than 8.26 ounces?
(e) A foreign company ordered 30 packages of cream cheese. There is a weight limit on international shipping. The maximum weight for international shipping is 245 ounces. Find the probability that this foreign company will receive their packages of cream cheese.
(a) 0.0228 (b) 0.2743 (c) 8.3645 (d) 0.1151 (e) 0.0336 (or 0.0475)
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