4. [14 pts] The life expectancy of a microwave oven is normally distributed with an average of 16.7 years, and a standard deviation of 3.1 years. Round all probabilities to 4 decimal places. a) Sketch and label a complete normal distribution for this situation (include values of 30): I -30=16.7-3.3.1 = 16.7-9.3 = 7.4 years 1 H-20 16.7-2.3.1 = 16.7-6.2 = 10.2 years 1 H- =16.7-3.1=13.6 years H = 16.7 years center of distribution H+ = 16.7+3.1 = 19.8 years I H+20=16.7+2 3.1 = 16.7+ 6.2 = 22.9 years I H+30=16.7+3.3.1 = 16.7+9.3 = 26.0 years 17.4 10.5 13.6 16.7 19.8 22.9 b) Find the probability of buying a microwave that lasts for more than 24 years. Label this value/shade in this area in the distribution above to show the connection to the probability you calculate.