1) We want to buy a certain refrigerator for home. We have been informed of a certain brand and it indicates that the life of these follows a normal distribution with a mean of 16 years and a variance of 4. a) What is the probability that if we buy one of these refrigerators it will last us more than 20 years? 2) IN THE PREVIOUS EXERCISE We want to buy a certain refrigerator for home. We have been informed of a certain brand and it indicates that the life of these follows a normal distribution with a mean of 16 years and a variance of 4. b) What is the probability that it will last between 10 and 14 years? 3) In a farm it has been determined that the weight of the egg production can be assimilated to a normal distribution of mean 175gr and variance 144gr2. We are going to classify them into Large (over 180), medium (from 170 to 180) and small (from 155 to 170). a) What percentage of eggs will we classify as "Large"? 4) IN THE PREVIOUS EXERCISE In a farm it has been determined that the weight of the egg production can be assimilated to a normal distribution of mean 175gr and variance 144gr2. We are going to classify them into Large (over 180), medium (from 170 to 180) and small (from 155 to 170). b) If we take a dozen "large" eggs, what is the probability that we will get one of more than 185 gr? 5) IN THE PREVIOUS EXERCISE In a farm it has been determined that the weight of the egg production can be assimilated to a normal distribution of mean 175gr and variance 144gr2. We are going to classify them into Large (over 180), medium (from 170 to 180) and small (from 155 to 170). c) In a box containing 12 dozen "large" eggs, what is the probability that more than half of the dozens contain an egg larger than 185g? 6) IN THE PREVIOUS EXERCISE In a farm it has been determined that the weight of the egg production can be assimilated to a normal distribution of mean 175gr and variance 144gr2. We are going to classify them into Large (over 180), medium (from 170 to 180) and small (from 155 to 170). d) Finally, a merchant buys 40% of the largest eggs from us. From what weight do we have to separate to take them? 7) A quality study has studied the pressure that a model of car wheels that was causing problems can withstand. It has been observed that a normal distribution can be approximated with a mean of 3.5 bars and a variance of 1.44 bars2. A company has manufactured 4000 of these wheels and has put a pressure of 3.7 bars. With this data, a) How many wheels are likely to burst and have to be replaced? 8) IN THE PREVIOUS EXERCISE A quality study has studied the pressure that a model of car wheels that was causing problems can withstand. It has been observed that a normal distribution can be approximated with a mean of 3.5 bars and a variance of 1.44 bars2. A company has manufactured 4000 of these wheels and has put a pressure of 3.7 bars. With this data, b) If we want to make sure that a maximum of 400 wheels can cause problems, what maximum pressure should we put in the tire when selling them? 9) PREVIOUS EXERCISE A quality study has studied the pressure that a model of car wheels that was causing problems can withstand. It has been observed that a normal distribution can be approximated with a mean of 3.5 bars and a variance of 1.44 bars2. A company has manufactured 4000 of these wheels and has put a pressure of 3.7 bars. All the wheels manufactured have been withdrawn except for 4 batches of 8 units each, which were already sold to a workshop. From factory quality, a communication has been made so that the pressure at which the wheels of these batches are placed is 2.7 bars. We accept that in a batch 2 units may fail under the indicated conditions, because in the event that more than 2 units fail, the total batch will have to be reimbursed to the workshop plus compensation. What is the probability that more than 2 wheels fail in a given lot and have to pay compensation