Exam 8: Sampling Distributions

Compute Probabilities of a Sample Proportion -Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for the afternoon shift $5 \%$ of all welds done will be substandard. If Smith checks 300 of the 7500 welds completed that shift, would it be unusual for Smith to find 30 or more substandard welds?

Describe the Distribution of the Sample Mean-Samples from a Population That Is Not Normal -A farmer was interest 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 on average in the next 40 rows down which he drives his tractor?

Provide an appropriate response. -The amount of time it takes a student to walk from her home to class has a skewed right distribution with a mean of 17 minutes and a standard deviation of $1.2$ minutes. If data were collected from 50 randomly selected walks, describe the sampling distribution of $\bar { x }$ , the sample mean time.

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 and it was noted that 248 homes were to be used as investment property, would this be unusual Answer Yes or No.

Compute Probabilities of a Sample Proportion -Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for the afternoon shift $5 \%$ of all welds done will be substandard. If Smith checks 300 of the 7500 welds completed that shift, what is the probability that he will find less than 20 substandard welds?

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 at least 175 homes are going to be used as investment property?

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 it has about 10,000 regular customers. Of those customers, $28 \%$ of them plant a vegetable garden in the spring. The greenhouse obtains a random sample of 800 of its customers. Is it safe to assume that the sampling distribution of $\hat { p }$ , the sample proportion of customers that plant a vegetable garden, is approximately normal? Answer Yes or No.

Describe the Sampling Distribution of a Sample Proportion -A simple random sample of size $\mathrm { n } = 450$ is obtained from a population whose size is $\mathrm { N } = 13,000$ and whose population proportion with a specified characteristic is $\mathrm { p } = 0.2$ . Describe the sampling distribution of $\hat { p }$ .

Describe the Sampling Distribution of a Sample Proportion -A national caterer determined that $87 \%$ of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000 . The 144 people are asked to sample the caterer's food. If $\hat { p }$ is the sample proportion saying that the food is delicious, what is the mean of the sampling distribution of $\hat { p } ^ { \text {? } }$

Describe the Sampling Distribution of a Sample Proportion -To assess attitudes towards issues that affect the residents of a village, the village randomly chose 800 families to participate in a survey of life attitudes. The village received 628 completed surveys. What is the sample proportion of completed surveys?

Describe the Sampling Distribution of a Sample Proportion -According to a study conducted in one city, $36 \%$ of adults in the city have credit card debts of more than $\$ 2000$ . A simple random sample of $\mathrm { n } = 100$ adults is obtained from the city. Describe the sampling distribution of $\hat { \text { p} }$ , the sample proportion of adults who have credit card debts of more than $\$ 2000$ .

Describe the Distribution of the Sample Mean-Samples from a Population That Is Not Normal -John has six bills of paper money in the following denominations: $\$ 1 , \$ 5 , \$ 10 , \$ 20 , \$ 50$ , and $\$ 100$ If he selects 3 bills at a time how many, how many groups can be formed?

Describe the Distribution of the Sample Mean-Samples from a Population That Is Not Normal -The ages of five randomly chosen cars in a parking garage are determined to be $7,9,3,4$ , and 6 years old. If we consider this sample of 5 in groups of 3 , how many groups can be formed?

Provide an appropriate response. -One year, professional sports players salaries averaged $\$ 1.6$ million with a standard deviation of $\$ 0.7$ million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $\$ 1.1$ million.

Describe the Distribution of the Sample Mean-Samples from a Population That Is Not Normal -John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3 bills at a time what is the probability of selecting a group that has an average value of equal to or less than $25

Provide an appropriate response. -The average score of all golfers for a particular course has a mean of 66 and a standard deviation of 5 . Suppose 100 golfers played the course today. Find the probability that the average score of the 100 golfers exceeded $67 .$

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 60 or more flights on average in the next 40 rows down which he drives his tractor?

Provide an appropriate response. -Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of 9.6. If 144 people are randomly selected, find the probability that their mean blood pressure will be less than $124 .$

Describe the Sampling Distribution of a Sample Proportion -If a population proportion is believed to be $0.6$ , how many items must be sampled to ensure that the sampling distribution of $\hat { p }$ will be approximately normal? Assume that the size of the population is $N=10,000$ .

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 at most 200 homes are going to be used as investment property?