(4) 11. The manager of a food market guarantees that none of his cartons of one dozen eggs will contain more than one bad egg. If a carton contains more than one bad egg, he will replace the whole dozen and allow the customer to keep the original eggs. The probability an individual egg is bad is .03. What is the probability that the manager will have to replace a given carton of eggs? (4) 12. What is the mean and standard deviation of the standard normal distribution? Mean = standard deviation = (12) 13. Lithium batteries for a cell phone currently last 10 hours on average before they need to be recharged. Apple is developing a new Lithium battery, the problem is they are much more expensive, that they hope will last longer before it needs to be recharged. In a sample of 20 of these new batteries placed in cellphones the average time the batteries lasted before needing to be recharged was 10.8 hours with a standard deviation of 3 hours a) At the .01 level do the new batteries last a statistically significant longer time? (p-value = 124) b) Based on the results for a) would these batteries be something you would purchase? Explain statistically