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Problem #1: The nicotine content (x) in a single cigarette of a particular brand has a normal distribution with mean 0.8 mg and a standard deviation of 0.1 mg. Suppose a random sample of 100 of these cigarettes are analyzed. a. Is the distribution of the sample mean normal? Why or why not? b. Specify the parameters (paClog) of the sampling distribution. c. Calculate the probability that the sample mean nicotine content exceeds 0.79 mg. (1. Calculate the probability that the sample mean nicotine content is less than 0.77 mg. e. Suppose the actual sample mean was calculated to be 0.75 mg. Construct and interpret a 95% condence interval for the true mean nicotine content. f. Based on your interval in e, does the data support the claim that the mean nicotine content is 0.8mg? Iustify your answer. . If the researchers want to estimate the true mean nicotine content with 99% condence and an error of 0.01mg, how many samples are needed