Standard normal table problems Part 3 If this helps These a

Standard normal table problems - Part 3

If this helps: These are hand calculated problems where you have to figure out if the random variable is X, Xbar, or Pbar. Then you have to label the top curve and shade the appropriate area. Shade the same area on the bottom Z curve and then use the appropriate Z formula and the standard normal table to find the answer. Problem: On the SAT, the average Writing score is 475 points and the average Mathematics score is 535 points. The standard deviation is 80 points on each part of the test. Now suppose 55 test takers are selected. 7% of the time the sample average Mathematics score should be less than what? (Remember the label.) Problem: The time it takes to bake a Betty Crocker Super moist Fudge Cake is normally distributed with a mean of 41 minutes and a variance of 58 minutes^2. Let baking time, in minutes, be represented by random variable X.

Solution

On the SAT, the average....

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.07      
          
Then, using table or technology,          
          
z =    -1.475791028      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    535      
z = the critical z score =    -1.475791028      
s = standard deviation =    80      
n = sample size =    55      
Then          
          
x = critical value =    519.0803503   [answer]  

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