The mean annual salary for Level 1 actuaries in the United States is about ($ 72,000). A

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The mean annual salary for Level 1 actuaries in the United States is about \(\$ 72,000\). A random sample of 45 Level 1 actuaries is selected. What is the probability that the mean annual salary of the sample is

(a) less than \(\$ 75,000\) and

(b) more than \(\$ 68,000\) ? Assume \(\sigma=\$ 11,000\).

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