Please help me with this statistics normal distribution question?

Posted on 2016-04-04 18:51:00 in Statistics by JOYER

Suppose the mass of a cigar is a Normal random variable. Assume a single cigar weighs 20 g on average with a standard deviation of 4 g. A tin of cigars contains exactly 10 cigars, with the weight of the packaging (excluding the cigars) also being a Normal random variable with mean 30 g and standard deviation 2 g. Assume all the random variables are independent. 
Q1: Calculate the variance of the weight of a tin full of cigars. 
Q2: If you buy 5 tins of cigars, what is the probability that the total weight of this purchase exceeds 1.2 kg? 
Q3: Suppose that a batch of contaminated leaves were used to manufacture a huge consignment of cigars, causing spores to grow randomly on some of these cigars. The factory desperately needs to find out what the average number of spores per cigar (𝜆) is. By quick examination of a very large number of samples, they were able to determine that 68 percent of the cigars had grown at least 1 spore. Estimate 𝜆. 
 

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