Question 1085822
<font color="black" face="times" size="3">We're in the xbar distribution (sample mean distribution, or distribution of sample means). In this case the center is at mu = 50 and the standard error is SE = s/sqrt(n) = 40/sqrt(100) = 40/10 = 4


This distribution is normally distributed because of the central limit theorem. The fact that n = 100 makes n > 30 true indicates that we can use this idea. 


Using a calculator, the value of P(45 < x < 55) is roughly 0.7887


Subtracting 1 from that value gives 1-0.7887 = 0.2113 which converts to 21.13%


That rounds to 21.1% so you have the correct answer. Nice work.


You can use an online tool such as <a href = "http://onlinestatbook.com/2/calculators/normal_dist.html">this one</a> to check your work. 
That specific calculator also provides the sketch of the shaded area.</font>