1. [8 pts] A manufacturer of compact fluorescent light bulbs advertises that the distribution of the lifespans of these light bulbs is nearly normal with a mean of 9,000 hours and a standard deviation of 1,000 hours. a. What is the probability that a randomly chosen light bulb lasts more than 9,400 hours? Define, draw and label the distribution and give your answer in a complete sentence. b. Let's say the distribution of the bulb lifespans is instead heavily skewed to the right. We want to select 40 bulbs and calculate their average lifespan. Write about each of the conditions needed to use the sampling distribution of a mean. c. What is the probability that the mean lifespan of 40 randomly chosen light bulbs is more than 9,400 hours? Define, draw and label the distribution and give your answer in a complete sentence.2. [7 pts] The Pew Research Center estimates that as of January 2014, 89% of 18-29-year-olds in the United States use social networking sites. a. For a sample size of 100, write about each of the conditions needed to use the sampling distribution of a proportion. b. Calculate the probability that at least 91% of 100 randomly sampled 18-29-year-olds use social networking sites. Define, draw and label the distribution and give your answer in a complete sentence. c. Calculate the probability that at least 91% of 500 randomly sampled 18-29-year-olds use social networking sites. Define, draw and label the distribution and give your answer in a complete sentence. Page 2