ues Degrees of freedom Sample/Population proportion X 1. A package of frozen vegetables has a label that says "contents 32 oz." However, the company that produces these packages knows that the we the weights are normally distributed with mean 32 will weigh? oz. and standard deviation 2 oz. If a package is chosen at random, what is the probability that it a) more than 35 oz.? 0) less than 30 oz.? c) between 30 and 35 oz.? 2. Suppose that the test scores for a college entrance exam are normally distributed with a mean of 450 and a standard deviation of 100. a) What percentage of those taking the exam score between 350 and 450? b) A student scoring above 400 is automatically admitted. What percent score above 400? c) The upper 5% receive scholarships. What score must a student make on the exam to receive a scholarship? 3. The heights of adult males are normally distributed with a mean height of 70 inches and a standard deviation of 2.6 inches. How high should the doorway be constructed so that 90% of the men can pass through it without having to bend? 4. The heights of college age men are known to be normally distributed with a mean of 68 in. and a standard deviation of 3 in. a) What is the probability that the mean height of a random sample of nine college men is betwee 67 and 69 inches? b) What is the probability that the mean height of a random sample of 100 college men is betwee 67 and 69 inches? c) Compare your answers to parts a and b. Was the probability in part b much higher? Why wou you expect this? d) Name the theorem you used to solve this problem. e) List the criteria to apply the theorem