Application Problems: Write your answer in four decimal places and do not write any words or place spaces before the answers. (For area and probability only) Example: 0.2354 or .2354. A recent study on world happiness, * W participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.2 and a standard deviation of 2.2. Find the probability that a randomly selected study participant's response was between 3 and 6. Your answer The heights of women aged 20 to 29 are * W approximately normal with mean 163 cm and standard deviation 6.9 cm. What is the zsore of women 183 cm tall? Round off answer to 2 decimal places Your answer A musical act expects the number of tickets sold for an upcoming concert to be normally distributed with a mean of 500 tickets and a standard deviation of 75 tickets. Answer the next two questions that follow. Your answer What is the probability that less than 350 * 2 tickets are sold? Your answer What is the probability that more than 400 * W tickets are sold? Your answer The length of life of an instrument produced * W by a machine has a normal distribution with a mean of 24 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last less than 18 months. Your answer The weights of boxes of a certain brand of * 2 cereals are normally distributed with a mean of 398 g and a standard deviation of 5 grams. Find the probability that a certain box selected at random weighs between 388 grams and 406 grams? Your answer The scale of scores for an IQ test are * 1* approximately normal with mean 100 and standard deviation 12. The organization MENSA, which calls itself the "high IQ society", requires a score of 125 or higher. What percent of adults would qualify for membership? Your answer The life of the bulbs has a normal distribution * 2 with a mean value of 1750 hours and a standard deviation of 350 hours. What is the probability that the light bulb will last for at least 2000 hours? Your answer The average score on an exam is normally * 2 distributed with a mean of 80 and a standard deviation of 8. What is the probability that a randomly selected paper has a score lower than 92? Your answer Suppose you work for a publishing company * '' and before launching a new magazine targeting fashion-oriented consumers, your boss wants to hold a meeting with perspective advertisers. Assume that annual expenditures on magazine ads in this genre are normally distributed with a mean of P 2,598,600 and a standard deviation of P250000. If the publisher wants to exclude companies with the smallest 9.85% in terms of annual expenditures on magazine ads from the sales meeting, what is the approximate minimum annual expenditure on magazine ads an advertiser would be required to have so that advertiser would be invited to the meeting? (Hint: What z-score corresponds to the minimum expenditure for advertisers that should be invited?) Your