MultiPassenger Vehicles MPVs produced by a manufacturer can

Multi-Passenger Vehicles (MPVs) produced by a manufacturer can accommodate seven adults. The load capacity of the passenger compartment is 1240 lb. if the weights of adults are distributed normally with a mean if 170LB and a standard deviation of 18lb, what is the probability that the mean weight of a sample of seven adults will exceed the maximum average with that the load capacity permits?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value = 1240/7 =   177.1428571      
u = mean =    170      
n = sample size =    7      
s = standard deviation =    18      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.049901314      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.049901314   ) =    0.146881744 [ANSWER]