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): H-30=16.7-3.3.1 = 16.7-9.3 7.4 years H-20 16.7-2.3.116.7-6.2=10.2 years H- =16.7-3.1=13.6 years H = 16.7 years I center of distribution H+ =16.7 3.1 = 19.8 years H+20=16.7+2 3.1 = 16.7+6.2 = 22.9 years H+30=16.7+3.3.1 = 16.7+9.3 26.0 years 7.4 10.5 12.7 13.6 16.7 14.5 22.9 24.0 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. P(x24) P (>2.35) = =1-P (z > 2.35) = 0.0094 c) Find the probability of buying a microwave that lasts for less than 13 years. P(x < 13) = P(x < -1.19) =1-P (2>-1.19) = 0.1170 d) Find the probability of buying a microwave that lasts between 12 and 19 years. P (1219) P(-1.516 23.985 The top 1% microwaves will last for more than 23.99 years. g) The middle 50% of microwaves last for how many years (note your solution is a range of values here). Round to 2 decimal places.