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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 H 30 16 7 3 3 1 16 7 9 3 H 20 16 7 2 3 1 16 7 6 2 H o 16 7 3 1 13 6 years H 16 7 years H 0 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 years I 10 2 years I 7 4 10 5 12 7 13 6 16 7 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 x 24 P z 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 Z 1 19 1 P z 1 19 0 1170 center of distribution d Find the probability of buying a microwave that lasts between 12 and 19 years P 12 x 19 P 1 516 Z 0 74 P Z 0 74 P Z 1 516 0 7704 0 0643 x 16 7 3 1 0 7061 e If a microwave manufacturer only wants to replace 10 of their microwaves with their warranty about how long should their warranty period be Round to the nearest year Sketch label this area value on your distribution from part a to make the connection to the value you calculate P z 1 2816 0 10 Their warranty period should be about 13 years x 12 73 f How long do the top 1 of microwaves last Round to 2 decimal places 16 7 2 35 x 16 7 2 35 3 1 X 23 985 19 8 22 9 24 0 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 2

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