Exam 7: Sampling Distributions

The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean has a mean of 36 oz.

The amount of time it takes to complete an examination has a left skewed distribution with a mean of 65 minutes and a standard deviation of 8 minutes.If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.So, the middle 95% of the sample means based on samples of size 64 will be between and .

The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is between 35.95 and 35.98 oz.is .

The standard error of the mean

In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

The mean score of all pro golfers for a course has a mean of 70 and a standard deviation of 3.0.Suppose 36 pro golfers played the course today.Find the probability that the mean score of the 36 pro golfers exceeded 71.

SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.A sample of 25 cans is to be selected.So, 95% of all sample meanswill be greater than how many grams?

The standard error of the population proportion will become larger

The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is less than 36.03 is .

SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4, 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

SCENARIO 7-1 The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken to estimate the mean study time for the population of all students. -Referring to Scenario 7-1, what is the probability that the sample mean differs from the population mean by less than 2 hours?

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million.

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.A random sample of 16 cars is selected.What is the probability that the sample mean is between 45 and 52 minutes?

The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be less than 82 minutes is .

A study at a college in the west coast reveals that, historically, 45% of the students are minority students.If a random sample of size 75 is selected, the probability is that between 30% and 50% of the students in the sample will be minority students.