Find the probability and interpret the results If convenient

Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was

$2.716 per gallon. A random sample of 34 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.699 and $2.727 that week? Assume sigmaequals=$0.042

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The probability that the sample mean was between

$2.699

and

$2.72 is?

(Round to four decimal places as needed.)

Solution

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    2.699      
x2 = upper bound =    2.727      
u = mean =    2.716      
n = sample size =    34      
s = standard deviation =    0.042      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u) * sqrt(n) / s =    -2.360147196      
z2 = upper z score = (x2 - u) * sqrt(n) / s =    1.527154068      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.009133843      
P(z < z2) =    0.936638648      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.927504805   [ANSWER]