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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)

2.  In one orchard, 20 trees are sampled and found to have an average production per tree of \(\overline{x} = 420.0 kg\) and a sample standard deviation of \(s = 72.4 kg\). Find a 90\% confidence interval for the average production per tree, \(\mu\), in the orchard.

a.  (391.0, 449.0)

b.  (392.0, 448.0)

c.  (393.0, 447.0)

d.  (394.0, 446.0)

d.  (395.0, 445.0)

3.  Say you know that a random variable x is distributed normally and that \(\sigma = 6.08\). If you're finding a 90% confidence interval for \(\mu\), how big must your sample be so that your margin of error is 1.25?

a.  25

b.  36

c.  50

d.  64

d.  100