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1. Let f(x) = 2e^(-(x-3)/c), 3 < x < infinity (zero otherwise) be a p.d.f. of a random variable X.
a. Find c
b. Find the CDF of X and sketch the CDF
c. Compute P(-5 < X < 10)
2. A candy maker produces mints that have a label weight of 30 grams. Assume that the distribution of the weights of these mints is N(30, 2^2).
a. Let X be the weight of a single mint selected at random from the production line. Find P(X > 32).
b. Suppose that 20 minutes are selected independently and weighted. Let Y equal the number of these mints that weigh less than 30 grams. Then find P(Y = 3).
c. Now, suppose that n = 100 mints are selected independently and weighted. Let Y equal the number of these mints that weigh less than 30 grams. Find the probability P(20 < Y <= 30) approximately. (Hint: Use CLT)
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This is called a one-time fling. About 10% of all adults deliberately do a opne-time fling and feel no guilt about it!
Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).
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It is reported in USA Today that the average flight cost nationwide is $342.59. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually less than $342.59. What are the appropriate hypoth..
Show how to generate a random variable from the exponential distribution function shown above. Show derivation of the equation.
Based on this sample, is Moe correct in his assertion? Write up formal commentary of results of your test.
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