Question

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.

Answer 1

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.