The average cost for two people to go to a movie is $21. The standard deviation

Question

The average cost for two people to go to a movie is $21. The standard deviation is $3. Assume the cost is normally distributed. Find the probability that at any given theater, the cost will be more than $23 for two people to go to the movie. Refer to the table of values (Area Under the Standard Normal Distribution) as needed. If necessary, round intermediate calculations to the nearest hundredth. The probability that at any given theater, the cost will be more than $23 for two people to go to a movie is %.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    23      
u = mean =    21      
          
s = standard deviation =    3      
          
Thus,          
          
z = (x - u) / s =    0.67      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.67   ) =    0.2514 = 25.14% [ANSWER]

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