Among U.S. cities with a population of more than 250,000 the moan one-way commut

Question

Among U.S. cities with a population of more than 250,000 the moan one-way commute time to work is 24.3 minutes The longest one-way travel time is in New York City. where the mean time is 38.5 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.2 minutes What percent of the New York City commutes are for loss than 26 minutes? (Round the Intermediate values to 2 decimal places. Round your answer to 2 decimal places ) What percent are between 26 and 34 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) What percent are between 26 and 45 minutes? (Round the Intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Explanation / Answer

b)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    26      
x2 = upper bound =    34      
u = mean =    38.5      
          
s = standard deviation =    7.2      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.74      
z2 = upper z score = (x2 - u) / s =    -0.63      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.0409      
P(z < z2) =    0.2643      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.2234   = 22.34% [ANSWER]  

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