how many of the loaves (rounded to the nearest loaf) had less than 8.8 g of wheat grains?

Question

A local bakery makes wheat bread. The number of grains of wheat in the bread is normally distributed, with mean 11.4 g and standard deviaton 1.3 g. This bakery sells 100 loaves of bread.

Answer 1

Sheily:

 

You ask "how many of the loaves (rounded......)....8.8 gms of wheat grains?

 

You have to careful, because this question can not be answered!!!  You have a sample of 100 loaves. As an extreme, you may have NO loaf that has less than 8.8 gms of grains or may be 26, who knows?  Any arbitrary number between 0 and 100.

 

All you can answer is what the "expected" number of loaves in a random sample of 100 containing those that ahve less than 8.8 gms of grains.  This you do by multiplying the probability Pr[ X < 8.8], X being the wheat grains in a loaf (in gms) by 100, the sample size.  PLEASE UNDERSTAND WHAT I AM SAYING.  Ask me as a comment if you need me to explain.

 

Now Pr[ X < 8.8] = Pr [ z = (X - 11.4)/1.3 < (8.8 - 11.4)/1.3] =  Pr[ z < -2].

 

Go to the weblink              http://www.danielsoper.com/statcalc3/calc.aspx?id=2

 

Enter z_score = -2.0 to get 0.02275.  Multiply by 100 to get the answer-----2.27 = 2, rounded to the nearest loaf.