Exam 8: Sampling Distributions

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3bills at a time what is the probability of selecting a group that has an average value of at least $26?

A national caterer determined that 87% of the people who sampled their food said that it was delicious. Arandom sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the^catererʹs food. If p is the sample proportion saying that the food is delicious, what is the mean of the sampling^distribution of p?

Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that forthe afternoon shift 5% of all welds done will be substandard. If Smith checks 300 of the 7500 welds completedthat shift, what is the probability that he will find more than 25 substandard welds?

Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 124.

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3bills at a time what is the probability of selecting a group that has an average value of between $40 and $45?

One year, professional sports players salaries averaged $1.9 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 averagesalary of the 100 players exceeded $1.1 million.

According to a study conducted in one city, $39 \%$ of adults in the city have credit card debts of more than $\$ 2000$ . A simple random sample of $n = 100$ adults is obtained from the city. Describe the sampling distribution of $p$ , the sample proportion of adults who have credit card debts of more than $\$ 2000$ .

A greenhouse in a tri-county area has kept track of its customers for the last several years and has determinedthat 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 p, the sample proportion of customersthat plant a vegetable garden in the spring?

A farmer was interested in determining how many grasshoppers were in his field. He knows that thedistribution of grasshoppers may not be normally distributed in his field due to growing conditions. As hedrives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows hefigures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of thefarmer will count 52 or fewer flights or 60 or more flights on average in the next 40 rows down which he driveshis tractor?

Assume that the heights of men are normally distributed with a mean of 70.7 inches and a standard deviationof 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height greater than71.7 inches.

What are the values of $\mu _{\bar { x }} \text { and } \sigma _{\bar { x }}$ for the sampling distribution of the sample mean shown?

The standard error of the mean is given by

The number of violent crimes committed in a day possesses a distribution with a mean of 2.2 crimes per dayand a standard deviation of 6 crimes per day. A random sample of 100 days was observed, and the meannumber of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.

John has six bills of paper money in the following denominations: $1, $5, $10, $20, $50, and $100 If he selects 3bills at a time how many, how many groups can be formed?

A national caterer determined that 87% of the people who sampled their food said that it was delicious. Arandom sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the^catererʹs food. Will the distribution of p, the sample proportion saying that the food is delicious, beapproximately normal?

The sampling distribution of the sample mean is shown. If the sample size is n = 16, what is the standarddeviation of the population from which the sample was drawn? Round to the nearest thousandth whereappropriate.

Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. Asample is drawn from this population of size 64. What is the standard error of the mean?

To assess attitudes towards issues that affect the residents of a village, the village randomly chose 800 familiesto participate in a survey of life attitudes. The village received 628 completed surveys. What is the sampleproportion of completed surveys?

A national caterer determined that 37% of the people who sampled their food said that it was delicious. Arandom sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the^catererʹs food. If p is the sample proportion saying that the food is delicious, what is the standard deviation of^the sampling distribution of p?

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were consideredinvestment 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?