Exam 8: Sampling Distributions

Compute Probabilities of a Sample Proportion -The National Association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that between 175 and 200 homes are going to be used as investment property

Describe the Distribution of the Sample Mean-Samples from a Population That Is Not Normal -A farmer was interested in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12 . What is the probability of the farmer will count 52 or fewer flights or 60 or more flights on average in the next 40 rows down which he drives his tractor?

Describe the Distribution of the Sample Mean-Samples from a Population That Is Not Normal -The owner of a computer repair shop has determined that their daily revenue has mean $\$ 7200$ and standard deviation $\$ 1200$ . The daily revenue totals for the next 30 days will be monitored. What is the probability that the mean daily revenue for the next 30 days will exceed $\$ 7000$ ?

Provide an appropriate response. -The amount of money collected by a snack bar at a large university has been recorded daily for the past five years. Records indicate that the mean daily amount collected is $1950 and the standard deviation is $500. The distribution is skewed to the right due to several high volume days (including football game days). Suppose that 100 days were randomly selected from the five years and the average amount collected from those days was recorded. Which of the following describes the sampling distribution of the sample mean

Describe the Sampling Distribution of a Sample Proportion -A greenhouse in a tri-county area has kept track of its customers for the last several years and has determined that $28 \%$ of its customers plant a vegetable garden in the spring. The greenhouse obtains a random sample of 1000 of its customers. What is the mean of the sampling distribution of $\hat { p }$ , the sample proportion of customers that plant a vegetable garden in the spring?

Provide an appropriate response. -The amount of corn chips dispensed into a 12 -ounce bag by the dispensing machine has been identified at possessing a normal distribution with a mean of $12.5$ ounces and a standard deviation of $0.1$ ounce. Suppose 400 bags of chips were randomly selected from this dispensing machine. Find the probability that the sample mean weight of these 400 bags exceeded $12.6$ ounces.