please help will rate The time it takes to bake a Betty Croc

please help will rate

The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally distributed with a mean of 38 minutes and a variance of 46 minutes^2. Let baking time, in minutes, be represented by random variable X.

P(x1 < X < 41) = 0.0930. Find x1. (Remember the label.)

Solution

For the left tailed area of x = 41:

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    41      
u = mean =    38      
          
s = standard deviation =    6.782329983      
          
Thus,          
          
z = (x - u) / s =    0.442325868      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   0.442325868   ) =    0.670873293

Thus, the left tailed area of x1 is 0.670873293 - 0.0930 = 0.577873293.

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For x1:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.577873293      
          
Then, using table or technology,          
          
z =    0.196455814      
          
As x = u + z * s,          
          
where          
          
u = mean =    38      
z = the critical z score =    0.196455814      
s = standard deviation =    6.782329983      
          
Then          
          
x1 = critical value =    39.33242816 MINUTES [ANSWER]