Sampling Distributions WS DIRECTIONS: SHOW ALL WORK! A final response following a calculation should be a sentence. Place a box around your final response. Round probability calculations to 4 decimal places. Round other numerical results including percents to two decimal places (e.g. 2.56 shoes, 18.49%). 1. 72.8% of all State U students receive some form of financial assistance. (a) In a random group of 50 State U students, what is the probability between 67.3% and 79.2% receive financial assistance? (b) In a random group of 75 State U students, what is the probability between 67.3% and 79.2% receive financial assistance? 2. Clutch size refers to the number of eggs laid by a bird during mating season. Suppose the mean clutch size for a brown-breasted woodpecker is 3.6 eggs with a standard deviation of 1.4 eggs. (a) Compute the probability that a randomly selected woodpecker lays more than 4 eggs. (b) Compute the probability that a randomly selected group of 24 woodpeckers lays more than 4 eggs on average. (c) Compute the probability that a randomly selected group of 36 woodpeckers lays more than 4 eggs on average. 3. Western Airlines typically cancels 1.2% of its flights annually. Given a random sample of 1000 flights, what is the likelihood less than 1% are canceled? 4. The mean time it takes students at State U to walk from their dorms to the quad is 10.6 minutes with a standard deviation of 3.1 minutes. Javier, as part of a project for his business statistics class, stopped 40 students he met on the quad that day and asked how long it took them to walk from their dorms. What is the probability the mean time is between 7.25 minutes and 12.15 minutes? 5. All manufacturing includes errors in measurement. The key is to minimize those errors. Suppose a chocolate chip company fills its bags with a mean of 24 ounces and a standard deviation of 0.6 ounces. The process is designed so that the weights are normally distributed. (a) Compute the probability that a randomly selected bag weighs less than 23.75 ounces. (b) Compute the probability a randomly selected sample of 16 bags has a mean weight of less than 23.75 ounces. (c) Compute the probability a randomly selected sample of 36 bags has a mean weight of less than 23.75 ounces. 6. Bear Island has 800 residents. 68% own at least one horse. In a random sample of 50 residents, what is the probability between 64.3% and 67.5% own at least one horse? 7. Engineers at NASA are testing a new heat shield that protects its vehicles upon re-entry into Earth's atmosphere. They know that temperatures upon re-entry are normally distributed with a mean of 1300 C and a standard deviation of 85 C. Conducting a test of 36 random simulations, what is the likelihood the mean re-entry temperature is between 1325.C and 1340'C ? 8. 8% of widgets manufactured by ACME are exported to factories in Asia and Europe. In a random sample of 220 widgets, what is the probability less than 6.6% are exported to Asia and Europe