please could you help me in this question In a supermarket t

please could you help me in this question

In a supermarket, the checkout time of casher service has a normal distribution. The average time is 3 minutes per customer with standard deviation 0.5 min. What is the probability that a customer\'s checkout time is longer than 4 minutes? What is the probability that a customer\'s checkout time is shorter than 2.5 minutes?

Solution

a)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    4      
u = mean =    3      
          
s = standard deviation =    0.5      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132 [answer]

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b)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    2.5      
u = mean =    3      
          
s = standard deviation =    0.5      
          
Thus,          
          
z = (x - u) / s =    -1      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -1   ) =    0.158655254 [answer]