More Practice - Sample Means Name: ___________________________ 1) Assume that a school district has 10,000 6th graders. In this district, the average weight of a 6th grader is 80 pounds, with a standard deviation of 20 pounds. Suppose you draw a random sample of 50 students. What is the probability that the average weight of the sampled students will be less than 75 pounds? 2) The average speed of winds in Honolulu, HI is 11.3 miles per hour. The standard deviation of the wind speeds is 3.5 miles per hour. Assume that the wind speeds follow a normal distribution. 3) a.) Find the probability that a single wind speed reading will exceed 13.9 mph. b) Find the mean and the standard deviation for the means of winds speeds if samples of size n = 9 are obtained. c) Find the probability that the mean of 9 wind speed readings will exceed 13.9 mph. Assume that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Suppose you take a random sample of 25 high school students and measure their IQ. a) What is the probability that the mean IQ from your sample will be 105 or higher? b) Now change your sample size to 64. What is the probability that the mean IQ from your sample will be 105 or higher? 4) You are the director of transportation safety for the state of Georgia. You are concerned because the average highway speed of all trucks may exceed the 60 mph speed limit. A random sample of 120 trucks shows a mean speed of 62 mph. Assuming the population mean is 60 mph and the population standard deviation is 12.5 mph, find the probability that the average speed of the sample is at least 62 mph. 5) A ski gondola in Bogus Basin Ski Resort carries skiers to the top of the mountain. Assume that it bears a plaque stating that the maximum capacity is 12 people or 2004 pounds. That capacity will be exceeded if 12 people have weights with a mean greater than 2004/12 = 167 pounds. Because men tend to weigh more than women, a worst-case scenario involves 12 passengers who are all men. Men have weights that are normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds (based on data from the National Health Survey). a) Find the probability that if an individual man is randomly selected, his weight will be greater than 167 pounds. b) Find the mean and the standard deviation for the mean weights of samples of 12 men. c) Find the probability that 12 randomly selected men will have a mean weight that is greater than 167 pounds (so that their total weight is greater than the gondola maximum capacity of 2004 pounds).