Let the random variable X represent the profit made on a ran

Let the random variable X represent the profit made on a randomly selected day by a small clothing store on Main Street. Assume X is Normal with a mean of $360 and a standard deviation of $50.

(a) What is P(X > $400)?

(b) The probability is approximately 0.6 that on a randomly selected day the store will

make less than how much?

Solution

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    400      
u = mean =    360      
          
s = standard deviation =    50      
          
Thus,          
          
z = (x - u) / s =    0.8      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.8   ) =    0.211855399 [answer]

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b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.6      
          
Then, using table or technology,          
          
z =    0.253347103      
          
As x = u + z * s,          
          
where          
          
u = mean =    360      
z = the critical z score =    0.253347103      
s = standard deviation =    50      
          
Then          
          
x = critical value =    372.6673552   [answer]