It is known that the national average price of a burrito is

It is known that the national average price of a burrito is dollar7 with standard deviation of dollar0.50. (a) What is the probability the sample mean of 64 burrito prices (anywhere in the nation) is greater than dollar7.20? (b) Suppose we find that an average price of a burrito among 64 mexican restaurants in Santa Barbara area to be dollar7.20. What does this finding say about how expensive a burrito is in Santa Barbara?

Solution

A)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    7.2      
u = mean =    7      
n = sample size =    64      
s = standard deviation =    0.5      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    3.2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   3.2   ) =    0.000687138 [ANSWER]

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b)

That says that the burrito in Santa Barbara is significantly more expensive that the national average burrito, because the probability of this happening is so small that it couldn\'t have happened by chance alone.