Exam 7: Sampling Distributions

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with $\mu$ = 110 grams and $\sigma$ = 25 grams.A sample of 25 vitamins is to be selected. -What is the probability that the sample mean will be less than 100 grams?

The owner of a fish market has an assistant who has determined that the weights of rainbow trout are normally distributed,with mean of 3.2 kilograms and standard deviation of 0.8 kilogram. -If a sample of 64 fish yields a mean of 3.4 kilograms,what is the probability of obtaining a sample mean this large or larger?

If the population distribution is unknown,in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

The amount of time it takes to complete an examination has a skewed-left 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.

Instruction 7.3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. -Referring to Instruction 7.3,what is the probability that the sample mean lifetime is more than 1,550 hours?

The standard error of the mean

Instruction 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 Instruction 7.4,90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

An unbiased estimator will have a value,on average across samples,equal to the population parameter value.

If the expectation of a sampling distribution is located at the parameter it is estimating,then we call that sampling distribution

In the uncommon case where the distribution is extremely skewed or has more than one mode,you may need sample sizes larger than 30 to ensure normality.

The standard error of the sampling distribution of a sample proportion is $\sqrt { \frac { p ( 1 - p ) } { n } }$ where p is the sample proportion.

The standard deviation of the sampling distribution of a sample proportion is $\sqrt { \frac { \pi ( 1 - \pi ) } { n } }$ where ? is the population proportion.

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine. -So,95% of the sample means based on samples of size 36 will be between______ and _________

If the population distribution is skewed,in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

If the population distribution is symmetric,the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 15 observations.

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

The amount of time required for an oil and filter change on a car is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.A random sample of 16 cars is selected. -So,90% of the sample means will be greater than what value?

At a computer manufacturing company,the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm.A random sample of 12 computer chips is taken.What is the standard error for the sample mean?

The amount of time required for an oil and filter change on a car 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 will be between 39 and 48 minutes?

Instruction 7.5 According to an article, 19% of the entire Australian population have high-speed access to the Internet. Random samples of size 200 are selected from the Australian population. -Referring to Instruction 7.5,the population mean of all the sample proportions is _________ .