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1.  The weight of fruit produced by apple trees in one season is known to have a normal distribution with standard deviation \(\sigma = 72.4 kg\). In one orchard, 20 trees are sampled and found to have an average production per tree of \(\overline{x} = 420.0 kg\). Find a 90\% confidence interval for the average production per tree, \(\mu\), in the orchard. I remind you that \(z_{90\%} = 1.645\)

a.  (399.4, 440.6)

b.  (397.4, 442.6)

c.  (395.4, 444.6)

d.  (393.4, 446.6)

d.  (391.4, 448.6)