Stats - see below

Question

A machine packs nails in cartons. The number of nails in a carton is approximately normally distributed with a mean of 700.5 and a standard of deviation of 20. Find the probability that a carton of nails has more than 690 nails. (I keep getting an answer of 0.700208 however that is not the right answer.) Thank you!

Answer 1

Start by calculating how many standard deviations away from the mean your number is. This is your Z score.

Z = (690-700.5)/20 = -.525

Now we have a possible source of error. Z scores in Z tables only go to 2 decimal places. Which might be .52 or .53 in this case. Looking up .52 and .53 in a Z table, You would get .6985 or .7019. If you plug in your number to a calculator, you get that .700208 number, which is probably more accurate.