Boxes of bran flakes are known to be normally distributed with a mean weight of 475g and a standard deviation of 10g.Calculate the probability of a box having a weight exceeding 485 grams. Calculate the probability that the mean weight of sixteen boxes will exceed 480g.
Use z-scores.
Formula for the first part:
z = (x - mean)/sd
With your data:
z = (485 - 475)/10
I'll let you finish the calculation.
Once you have the z-score, check a z-table for the probability. (Remember the problem is asking "weight exceeding" 485 grams.)
Formula for the second part:
z = (x - mean)/(sd/√n)
With your data:
z = (480 - 475)/(10/√16)
I'll let you finish the calculation.
Once you have the z-score, check a z-table for the probability. (Remember the problem is asking "mean weight... will exceed" 480 grams.)
I hope this helps and will get you started.