Hello, I am struggling with the following questions over uniform, normal and exponential distributions. I have attached problems below.

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2. The uniform distribution The Transportation Security Administration (TBA) collects data on wait time at each of its airport security checkpoints. For ights departing from Terminal 1 at John F. Kennedy International Airport (JFK) between 3:00 and 4:00 PM on Wednesday, the mean wait time is 10 minutes, and the maximum wait time is 12 minutes. [Source: Transportation Security Administration, summary statistics based on historical data collected between February 18, 2008, and March 17, 2008.] Assume that x, the wait time at the Terminal 1 checkpoint at JFK for ights departing between 3:00 and 4:00 PM on Wednesday, is uniformly distributed between 8 and 12 minutes. Use the Distributions tool to help you answer the questions that follow. \fThe height of the graph of the probability density function f(x) varies with x as follows (round to four decimal places): x Height of the Graph of the Probability Density Function You are flying out of Terminal 1 at JFK on a Wednesday afternoon between 3:00 and 4:00 PM. You get stuck in a trafc jam on the way to the airport, and if it takes you longer than 11 minutes to clear security, you'll miss your ight. The probability that you'll miss your ight is V . The mean wait time is V minutes, and the standard deviation is V . 3. Probability computations using the standard normal distribution The average starting salary offer for accounting majors who graduated in 2007 was $46,292. [Source: National Association of Colleges and Employers, Salary Survey, Fall 2007.] Assume that x, the starting salary offer for accounting majors in the class of '07, is normally distributed with a mean of $46,292 and a standard deviation of $4,320. The probability that a randomly selected accounting major from the class of '07 received a starting salary offer greater than $45,000 is The probability that a randomly selected accounting major received a starting salary offer between $45,000 and $52,350 is V . What percentage of accounting majors received a starting offer between $38,500 and $45,000? 0 6.68% O 93.32% 0 65.38% 0 34.52% Twenty percent of accounting majors were offered a starting salary greater than v . 4. The normal distribution An automobile battery manufacturer offers a 29/46 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 29 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 29 months but within 46 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that x, the lifetime of its auto batteries, is normally distributed with a mean of 36 months and a standard deviation of 4.5 months. If the manufacturer's assumptions are correct, it would need to replace V of its batteries free of charge. The company nds that it is replacing 6.81% of its batteries free of charge. It suspects that its assumption about the standard deviation of the life of its batteries is incorrect. A standard deviation of V results in a 6.81% replacement rate. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't qualify for free replacement but do qualify for the prorated credit? 0 91.53% 0 43.19% 0 1.66% O 48.34% 7. The exponential distribution An economist studied a large data set of Mexican consumer prices covering episodes of both high and low inflation. One of the goods in the study was coffee. When the inflation rate was low, an average of 3.4 changes in the price of coffee occurred each year. When the inflation rate was high, the price of coffee changed more frequently-an average of 9.2 times each year. [Source: E. Etienne Gagnon, Price setting during low and high inflation: Evidence from Mexico, International Finance Discussion Papers, No. 896 (City: Board of Governors of the Federal Reserve System, 2007).] The expected number of coffee-price changes in a 1-month period is when inflation is low and when inflation is high. Assume that y, the number of price changes in any 1-month period, is described by a Poisson probability distribution with a mean equal to one of the values you just calculated (depending on whether the inflation rate is high or low). Then x, the number of months between consecutive price changes, is exponentially distributed with a mean of when inflation is low and a mean of when inflation is high.The probability that the price of coffee remains fixed for more than 4 months is when inflation is low and when inflation is high. If the probability that the price of coffee stays the same for 2 months or less is about 0.44, is Mexico's inflation rate high or low? O High O Low If Mexico is in a low inflation episode, the variance of x is