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

. It is known that the national average price of a burrito is $7 with standard deviation of $0.50. (a) What is the probability the sample mean of 64 burrito prices (anywhere in the nation) is greater than $7.20? (b) Suppose we find that an average price of a burrito among 64 mexican restaurants in Santa Barbara area to be $7.20. 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)

As the probability of that event is low (as in part a), then we can say that the burritos in Santa Barbara are significantly more expensive that the national average.