1 Consider the following sample of nine wait times measured

1. Consider the following sample of nine wait times measured in seconds at a drive through coffee shop. The population mean and standard deviation are 100 and 20 respectively.

125 95 66 116 99 91 102 51 110

a. What is the size of the sampling error in this case?

b. What is the probability that the average wait time would be between 90 and 95 seconds?

c. What is the probability that a customer waits more than 65 seconds?

Solution

a)

getting the sample mean,

X = 95

Thus, the sampling error is

Sampling error = X - u = 95 - 100 = -5 [ANSWER]

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b)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    90      
x2 = upper bound =    95      
u = mean =    100      
          
s = standard deviation =    20      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.5      
z2 = upper z score = (x2 - u) / s =    -0.25      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.308537539      
P(z < z2) =    0.401293674      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.092756136   [ANSWER]

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c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    65      
u = mean =    100      
          
s = standard deviation =    20      
          
Thus,          
          
z = (x - u) / s =    -1.75      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.75   ) =    0.959940843 [ANSWER]