Coal is carried from mines to power plants in hopper cars on

Coal is carried from mines to power plants in hopper cars on a long train. Weights of coal loaded into a car are normally distributed with mean mu = 75 tons and standard deviation sigma = 0.8 tons. What is the probability that 20 cars chosen at random will have a mean load weight of less than 74.5 tons of coal? What is P(-1.23

Solution

5.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    74.5      
u = mean =    75      
n = sample size =    20      
s = standard deviation =    0.8      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.795084972      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.795084972   ) =    0.002594304 = 0.0026, OPTION B [answer]

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