Find the indicated area under the standard normal curve between z = -3 and z = 3.2. Assume that the heights of men in the US are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The height requirement for men into the US ARMY is between 60 inches and 80 inches. If a man is randomly selected, what is the probability that his height is between 60 and 80 inches? Assume that blood pressure readings are normally distributed with μ = 111 and σ = 7. A researcher wishes to select people for a study but wants to exclude the top and bottom 20 percent. What would be the upper (part b) and lower (part a) readings to qualify people to participate in the study? a. Find the highest blood pressure reading a person can have and be in the lowest 20% (lower reading)? b. Find the lowest blood pressure reading a person can have and be in the highest 20% (upper reading)? The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. If 25 women are randomly selected, find the probability that they have a mean pregnancy less than 261 days. Note: You must justify the use of the normal distribution. Hint: use the central limit theorem. Assume that the salaries of elementary school teachers in the United States has mean $62,000 and a standard deviation of $5,000. If 36 teachers are randomly selected, find the probability that their mean salary is greater than $60,000. You must justify the use of the standard normal distribution. Hint: use the central limit theorem. A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 40 bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 50 hours. Test the manufacturer's claim. Use α = 0.05. A manufacturer claims that the mean lifetime of its fluorescent bulbs is more than 1000 hours. A homeowner selects 40 bulbs and finds the mean lifetime to be 1020 hours with a standard deviation of 100 hours. Test the manufacturer's claim. Use α = 0.04. A local brewery distributes beer in bottles labeled 24 ounces. A government agency thinks that the brewery is cheating its customers. The agency selects 50 of these bottles, measures their contents, and obtains a sample mean of 23.7 ounces with a standard deviation of 0.70 ounce. Use a 0.01 significance level to test the agency's claim that the brewery is cheating its customers.