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*Find:*

*A. P (Z ≤ -1.43)*

*B. P (Z > 2.02)*

*C. P (-2.13 ≤ Z ≤ 0.47)*

*D. Z* Such that P (Z > Z*) = 0.57*

*E. Z* Such that P (-Z* < Z < Z*) = 0.48*

*F. If X ~ N (**μ=80, σ=5), P(X>88)*

*G. **If X ~ N (μ=80, σ=5),** X* Such that P(X<X*) = .22*

*2.*

*When an employee of a certain company is selected at random the probability that the employee is single is ***.30***, the probability that the employee owns stocks unit bonds is ***.40***, and the probability that an employee is married and owns stocks and bonds is .***18**

*Fill in a joint probability table for the categories of marital status and stock-and-bond ownership.*

*What is the probability that an employee does not own stocks and bonds?*

*What is the probability that a single employee owns stocks and bonds?*

*What is the probability that a stock-and-bond owner is single?*

*What is the probability that an employee is a single stock-and-bond owner?*

*What is the probability that an employee is single or owns stocks and bonds?*

*3.*

*Suppose that ***40%*** of all credit card holders pay off their balances in full each month. If ***6*** such credit card holders are selected randomly (and independently), use the binomial probability table to find the probability that:*

*Exactly 3 pay off in full each month*

*Fewer than 4 pay off in full.*

*More than 2 pay off in full.*

*At least 2 but no more than 4 pay off in full.*

*Answer (D) if 70% pay off in full each month.*

*4.*

*A. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of ***67*** years and a standard deviation of ***4.5*** years. What proportion of the plan recipients would receive payments beyond age ***75***?*

*B. What is the probability that, in a sample of ***12 ***participants, exactly ***3 ***receive payments beyond year ***75***?*