One factory produces batteries of a certain type for use in laptops which it packs in packs of 20. According to factory data, the lifetime of a battery of this type can be considered to follow the normal distribution with an average value of =4 hours and a standard deviation =0.5 hours. Also, according to the specifications set by the European Union, if a battery of this type has a life of less than 3 hours, it is considered defective. Based on these data:

According to a new Community Directive, the manufacturer is obliged to indicate on the packaging the minimum battery life and will be subject to penalties in case more than 7% of the batteries last less than the indicated time. Calculate the time that should be indicated on the packaging so that the manufacturer does not suffer penalties.

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