The weight of bags of pretzels are normally distributed with a mean of 150 grams and a standard deviation of 5 grams. Bags in the upper 4.5% are too heavy and must be repackaged. Also, the bags in the lower 5% do not meet the minimum weight requirement and must be repackaged. What is the range of weight for a pretzel bag that does not need to be repackaged?

Question

The weight of bags of pretzels are normally distributed with a mean of 150 grams and a standard deviation of 5 grams.  Bags in the upper 4.5% are too heavy and must be repackaged. Also, the bags in the lower 5% do not meet the minimum weight requirement and must be repackaged. What is the range of weight for a pretzel bag that does not need to be repackaged? 
I can't figure out how to set up this problem, I thought this might have been a hypothesis test problem and I drew my bell curve, but now I'm stuck, please help!

PsyDAG · Answer

Z = (score-mean)/SD

Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportions/probabilities (.045 and .05) and their Z scores. Insert data into equation above to solve for scores.