Exam 8: Sampling Distributions

Professor Whata Guy surveyed a random sample of 420 statistics students. One of the questions was ʺWill youtake another mathematics class?ʺ The results showed that 252 of the students said yes. What is the sample^proportion, p of students who say they will take another math class?

A simple random sample of size n=1320 is obtained from a population whose size is N=1,400,000 and whose population proportion with a specified characteristic is p=0.46 . Describe the sampling distribution of $\hat { p }$ .

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 less than 20 substandard welds?

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

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 most200 homes are going to be used as investment property?

The ages of five randomly chosen cars in a parking garage are determined to be 7, 9, 3, 4, and 6 years old. If weconsider this sample of 5 in groups of 3, what is the probability of the population mean falling between 5.5 and6.5 years?

Furnace repair bills are normally distributed with a mean of 267 dollars and a standard deviation of 20 dollars.If 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 267dollars and 269 dollars.

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will exceed $7000?

If a population proportion is believed to be 0.6, how many items must be sampled to ensure that the sampling^distribution of p will be approximately normal? Assume that the size of the population is N = 10,000.

The ages of five randomly chosen cars in a parking garage are determined to be 7, 9, 3, 4, and 6 years old. If weconsider this sample of 5 in groups of 3, what is the probability of the population mean being more than 6years?

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 equal to or less than $25?

A random sample of size n is to be drawn from a population with μ= 600 and σ = 300. What size samplewould be necessary in order to ensure a standard error of 20?

The sampling distribution of the sample mean is shown. If the sample size is n = 36, what is the standarddeviation of the population from which the sample was drawn? Round to the nearest thousandth whereappropriate.

The ages of five randomly chosen cars in a parking garage are determined to be 7, 9, 3, 4, and 6 years old. If weconsider this sample of 5 in groups of 3, how many groups can be formed?

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

The amount of money collected by a snack bar at a large university has been recorded daily for the past fiveyears. Records indicate that the mean daily amount collected is $4000 and the standard deviation is $450. Thedistribution is skewed to the right due to several high volume days (including football game days). Supposethat 100 days were randomly selected from the five years and the average amount collected from those dayswas recorded. Which of the following describes the sampling distribution of the sample mean?

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will exceed $7500?

The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will be between $7000 and $7500?

A farmer was interest in determining how many grasshoppers were in his field. He knows that the distributionof grasshoppers may not be normally distributed in his field due to growing conditions. As he drives histractor down each row he counts how many grasshoppers he sees flying away. After several rows he figuresthe mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer willcount 52 or fewer flights on average in the next 40 rows down which he drives his tractor?