I. For a normally distributed population with a mean=50 and standard deviation=10, answer the following questions. 1. What proportion of scores: a. falls between the mean and a score of 47? b. is higher than 47? c. is lower than 53? d. is between 35 and 65? e. is between 40 and 47? f. is above 72? g. is below 31? h. is between 55 and 62? 2. What score do you need to be in the top 15% of the population distribution? 3. What score do you need to be in the bottom 5% of the population distribution? 4. What is the probability of selecting a score less than 55?

II. A random sample of 800 is selected from a population with a mean=100 and a standard deviation=10. If we select a sample from that population: 1. What is the probability that the sample mean would be: a. less than 98? b. more than 102? c. between 98 and 102? 2. What are the highest and the lowest sample means that you would find in the sampling distribution?

III. A criminologist wants to estimate the mean number of violent crimes per day for a particular year. He observes a random sample of 50 days and obtains a mean number of crimes per day of 1.3 crimes and a standard deviation of 1.7. 1. What proportion of scores: a. falls between 1 & 1.3? b. falls below 2? c. is between 2 & 3 d. is greater than 1? 2. What score do you need to be in the top 10% of the sample distribution? 3. What is the probability of selecting another sample with a mean: a. less than 1.1? b. more than 1.9? c. between 1 and 2? 4. What score do you need to be in the bottom 5% of the sampling distribution? 5. What are the highest and the lowest sample means in the sampling distribution?