Exam 8: Sampling Distributions

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 $\$ 7500$ ?

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 between $40 and $45

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 be between $\$ 7000$ and $\$ 7500$ ?

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 more than 25 substandard welds?

Provide an appropriate response. -The number of violent crimes committed in a day possesses a distribution with a mean of 3.8 crimes per day and a standard deviation of 2 crimes per day. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.

Describe the Sampling Distribution of a Sample Proportion -A national caterer determined that $37 \%$ 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 standard deviation of the sampling distribution of $\hat { p }$ ?

Provide an appropriate response. -Furnace repair bills are normally distributed with a mean of 271 dollars and a standard deviation of 15 dollars. If 36 of these repair bills are randomly selected, find the probability that they have a mean cost between 271 dollars and 273 dollars.

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 between 10 and 20 substandard welds?

Provide an appropriate response. -The standard error of the mean is given by

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, what is the probability of the population mean being more than 6 years

Provide an appropriate response. -Suppose a population has a mean weight of 180 pounds and a standard deviation of 25 pounds. A sample of 100 items is drawn from this population. What is the standard error of the mean?

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, what is the probability of the population mean falling between 5.5 and 6.5 years

Provide an appropriate response. -Assume that the heights of men are normally distributed with a mean of $67.9$ inches and a standard deviation of $2.1$ inches. If 36 men are randomly selected, find the probability that they have a mean height greater than $68.9$ inches.

Describe the Sampling Distribution of a Sample Proportion -A simple random sample of size $n = 1460$ is obtained from a population whose size is $\mathrm { N } = 1,400,000$ and whose population proportion with a specified characteristic is $\mathrm { p } = 0.57$ . Describe the sampling distribution of $\hat { p }$ .

Provide an appropriate response. -According to the law of large numbers, as more observations are added to the sample, the difference between the sample mean and the population mean

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 at least $26

Provide an appropriate response. -Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of $9.6$ . A sample is drawn from this population of size 64. What is the standard error of the mean?

Describe the Sampling Distribution of a Sample Proportion -Professor Whata Guy surveyed a random sample of 420 statistics students. One of the questions was "Will you take another mathematics class?" 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?

Provide an appropriate response. -A random sample of size $\mathrm { n }$ is to be drawn from a population with $\mu = 500$ and $\sigma = 100$ . What size sample would be necessary in order to ensure a standard error of 25 ?

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. Will the distribution of $\hat { p }$ , the sample proportion saying that the food is delicious, be approximately normal? Answer Yes or No.