Two phone batteries are to be tested for how they last (i.e., lifetime). Phone battery A has a lifetime that is normally distributed with mean 4.1 and standard deviation 1.6. Phone battery B has a lifetime that is normally distri mean 3.7 and standard deviation 1.5. Suppose that 100 batteries of each kind are tested. Hint: for this problem, you may find your notes from chapter 5 and 6 useful. (a) By the Central Limit Theorem, A is normally distributed with mean [ and standard deviation (b) By the Central Limit Theorem, B is normally distributed with mean (c) By the Central Limit Theorem, A - B is normally distributed with mean and standard deviation and standard deviation

A survey was conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. The results are summarized in the following table. only parts 4-7 iv) Can you spot a country which contributes negatively to the association? If yes, explain how. v) The standard deviation of the percent of teens who have used marijuana is 15.55% and it is 10.24% for the percent who have used other drugs. Calculate the correlation between the percent of teens who have used marijuana and the percent who have used other drugs. Show the ”by hand” formula you may use. vi) What does the correlation coefficient confirm or specify? vii) Do these results allow you to say that marijuana is a ”gateway drug”, that is, that marijuana use leads to the use of other drugs? Explain

Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?

You're working on a data sets involving the survival times of mice that were induced with cancer then treated with a new experimental drug. The mean of your data is 242.3 days with a standard deviation of 50.6 days. Unfortunately you've just learned that ALL your data is wrong. The initial day of the study was input improperly - and in fact the data you have is all 4 days less than it should be. When the data are corrected, what will be the value of the standard deviation?