Question 1161606: The average number of
milligrams (mg) of sodium in a certain brand of low-salt
microwave frozen dinners is 660 mg, and the standard
deviation is 35 mg. Assume the variable is normally
distributed.
a. If a single dinner is selected, find the probability that
the sodium content will be more than 670 mg.
b. If a sample of 10 dinners is selected, find the probability that the mean of the sample will be larger than
670 mg.
c. Why is the probability for part a greater than that for
part b?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z>(x-mean)/sd
=(670-660)/35
=10/35 or 0.286
this probability is 0.3875
for 10 dinners, the formula becomes z=(x bar-mean)/sigma/sqrt(n)
and z> 10*sqrt(10)/35=0.90
that probability is 0.1840
It is much more difficult for the average of 10 things to all be in the same direction compared to a single one.If there is one extreme value, the next probably will be less extreme or even in the other direction.
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