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For a Normal Distribution, \( \mu=12 \) and \( \sigma=1.5 \). Answer questions 7 thru 10 based on this information. (40 points) 7. What is \( \mathrm{P}(10.5 \leq \mathrm{X} \leq 15) \) ? Show all the relevant work. If using Excel, you must show all the relevant Excel formulae used. (10 points) 8. What is \( \mathrm{P}(\mathrm{X} \geq 15) \) ? Show all the relevant work. If using Excel, you must show all the relevant Excel formulae used. (10 points) 9. What is \( \mathrm{P}(\mathrm{X} \leq 10.5) \) ? Show all the relevant work. If using Excel, you must show all the relevant Excel formulae used. (10 points) 10. Given that the probability to realize a value less than ' \( \mathrm{X} \) ' is \( 0.8 \), find the value of ' \( \mathrm{X} \) '. Show all the relevant work. If using Excel, you must show all the relevant Excel formulae used. (10 points)

For a Normal Distribution, ?=12 and ?=1.5 P(10.5?X?15)=0.8186 P(X?15)=0.0228