1. The random variable X is uniformly distributed between 10 and 16. a) Graph the probability density function. b) Graph the cumulative probability function. c) Calculate P (X < 13) d) Calculate P (10 < X < 16) e) Calculate E (X). f) Calculate Var (X) 2. The label of a bottle of detergent indicates a capacity of 12 ounces (ounces: 16 ounces = 1 pound = 0.45 kg.) The production line fills the bottles so uniform according to the following density function: f(x) = 8 if 11.975 < x < 12.1; 0 otherwise. a) What is our interpretation of the number 8? b) What is the probability that a bottle contains between 12 and 12.05 ounces? c) Quality control accepts bottles that contain more or less 0.02 ounces of detergent from the number listed on the label. What is the probability that a bottle of detergent does not meet this condition? 3. The uniform distribution as well as the normal distribution are forms that are called parametric. Regarding the probability density function, explain the meaning of this feature? (Why is it so convenient)

8. The average stock price of the companies that make up the S&P 500 index is $30, and the standard deviation of $8.20 (old figures from 2003). Suppose the stock price is normally distributed (which might be reasonable). a) What is the probability that the stock price of a company is at least $40? b) What is the probability that the price of a company's stock will be less than $20? c) What must be the minimum share price for the company to be part of the 10% most rated? 9. In January 2003, an American employee spent an average of 77 hours browsing Internet during working hours. Assume that the internet connection time be normally distributed and the standard deviation equal to 20 hours. a) What is the probability that a randomly selected employee passes less than 50 hours surfing the internet? b) What percentage of employees spend more than 100 hours on the Internet? c) A person is considered a significant user if he or she is among the 20% using the internet the most. How many hours should a person spend on Internet to be considered a heavy user? 10. When you sign your credit card subscription agreement, do you read it carefully? For me the answer is no. During a survey, the question was asked following: "How carefully do you read a credit card subscription contract? credit? The results showed that 44% read every word of the contract, 33% the read carefully enough to understand it, 11% just glanced at it and 4 % did not read it at all. (Note - this is the normal approximation of binomial probabilities. That is to say, the basic variable is distributed according to the law binomial. See section 6.3.) a) in a sample of 500 people, how many people on average would say that they read every word of the contract? b) in a sample of 500 people, what is the probability that at most 200 people say read every word of the contract? c) in a sample of 500 people, what is the probability that at most 200 people say they don't read the contract? 13. The lifespans of light bulbs manufactured by a company have an average of 1,200 hours and a standard deviation of 400 hours. The probability distribution of this variable obeys the normal law. Suppose you buy 9 bulbs; you can consider as a random sample from that manufacturer's production. a) What is the mean of the sample mean? b) What is the variance of the sample mean? c) What is the standard deviation of the sample mean? d) What is the probability that the sample mean exceeds 93.0 units? 14. The average sale price for condominiums in the town of Green Valley was $215,000. (population average). The population standard deviation was $ 25,000.n researcher took a random sample of size 100 units. a) What is the probability that the sample mean is greater than $ 210,000? b) What is the probability that the sample mean is greater than $ 213,000 but less than $217,000? c) Without doing the calculations, determine which of the following intervals would contain the sample mean: $213.00 to $215,000; $214,000 to $216,000; $ 215,000 to $217,000; $216,000 to $218,000 d) Suppose a friend suggests to you that the calculations you have just made do not are invalid because this variable - The average selling price for condominiums in the town of Green Valley - does not obey normal law. What would your answer be?