Applying the central limit theorem to find probability example 2

[@dmcguckian]

There is a tiny error at the very end of the video (at about the 7th minute) after I have found the area from the z-table. When subtracting my table area from 0.5000, I somehow make a typo in the last digit. I subtract 0.4984 from 0.5000 instead of subtracting 0.4986. Everything prior to that is correct, so just finish the problem by doing 0.5000 - 0.4986.

[@BLVJOHN316]

Thank you and love your clear instructions! Due to the typo error, the last calculation was wrong and it lead to the wrong answer. Z value supposed to be 0.4986 and the correct answer is 14%.

[@dmcguckian]

Yes, you're right. I have that correction under the video at my website, but I forgot to put it here. It is in the video description though. Thanks!

[@bobdong9091]

Clear，Concise，Cool💪

[@mahraqureshi5808]

I have Question why x-bar is higher than 74,000 ? could you please explain

[@dmcguckian]

The curve represents the distribution for x-bar when n is 31. We are asked about the probability that a random sample of 31 has a mean greater than 74,000.

[@kiaracompton6813]

why isn't it 1 - .4986? Aren't u still subtracting from 1 since 1 is the area under the curve & .4986 accounts for the area to the left of 74k therefore, to find shaded area u need to subtract value from 1

[@dmcguckian]

You are right that the total area under the curve is 1. Since the curve is symmetric, the total area in half the curve is 0.5000. The z table I used gives the are from the z score you look up to the mean of zero. Some tables give the area from the z score to negative infinity. I think you may be thinking of that type of z table. There are many z table designs. You need to know how each one reads to use it in these problems. You can learn about the table used here by watching this set of videos: kzbin.info/www/bejne/fKjPdWqgebd1faM

[@charbelhaddad6724]

Why we did not substract 1-0.4986?

[@dmcguckian]

Hi Charbel, it might be correct to do that on your z table. It depends on the table you are using. For example if our table gave us the area from the z score to negative infinity, then you would calculate 1-0.9986 as your final answer. My z table gives the area from 0 to 2.98 as 0.4986. From 0 to infinity is 0.5000 under a z curve, so we subtract 0.4986 from 0.5000

[@MuhammedIsmael-h2l]

your z score table and mine are different

[@BrewsandViewsKe]

Me too.

[@dmcguckian]

All z tables are unique. You have to determine what area your table provides under the curve to determine how to use it. My videos use a table that gives the area from 0 to the z score looked up. Some provide the area from the z score to infinity. Others provide the area between two z scores. Others give the area from the z score to negative infinity. It doesn't matter which table you use. You just have to use it correctly depending on what your table provides.