Exam 17: Sampling Distribution Models

The weight of crackers in a box is stated to be 450 grams.The amount that the packaging machine puts in the boxes is believed to have a Normal model with mean 465 grams and standard deviation 30 grams.What is the probability that the mean weight of a 50-box case of crackers is below 450 grams?

If we imagine all the possible random samples of 150 students at this university,99.7% of the samples should have means between what two numbers?

Some real estate specialists estimate that the length of time people live in a house has a mean of 10 years and a standard deviation of 3 years.A random sample of 200 families was chosen and surveyed.Let Represent the mean number of years that those families had lived in their house.Describe the sampling distribution model of this mean.

A sample is chosen randomly from a population that was strongly skewed to the right.Describe the sampling distribution model for the sample mean if the sample size is small.

Assume that 32% of students at a university wear contact lenses.We randomly pick 300 students.Describe the sampling distribution model of the proportion of students in this group who wear contact lenses.

A restaurant's receipts show that the cost of customers' dinners has a skewed distribution with a mean of $54 and a standard deviation of $18.What is the probability that the next 100 customers will spend an average of less than $50 on dinner?

Researchers believe that 6% of children have a gene that may be linked to a certain childhood disease.In an effort to track 50 of these children,researchers test 950 newborns for the presence of this gene.What is the probability that they find enough subjects for their study?

A candy company claims that its jelly bean mix contains 15% blue jelly beans.Suppose that the candies are packaged at random in small bags containing about 200 jelly beans.What is the probability that a bag will contain more than 20% blue jelly beans?

If the students toss the coin 100 times each,about 95% should have proportions between what two numbers?

In a large class,the professor has each person toss a coin 200 times and calculate the proportion of his or her tosses that were tails.The students then report their results,and the professor records the proportions.One student claims to have tossed her coin 200 times and found 58% tails.What do you think of this claim? Explain your response.

A hair stylist believes the distribution of her tips is Normal,with a mean of $10.50 and a standard deviation of $6.25.What is the probability that her 15 clients this weekend will tip an average of less than $13?

When a truckload of oranges arrives at a packing plant,a random sample of 125 is selected and examined.The whole truckload will be rejected if more than 8% of the sample is unsatisfactory.Suppose that in fact 11% of the oranges on the truck do not meet the desired standard.What's the probability that the shipment will be accepted anyway?

If the students toss the coin 50 times each,about 68% should have proportions between what two numbers?

Statistics from a weather centre indicate that a certain city receives an average of 23 inches of snow each year,with a standard deviation of 3 inches.Assume that a Normal model applies.A student lives in this city for 4 years.Let Represent the mean amount of snow for those 4 years.Describe the sampling distribution model of this sample mean.

Automatic teller machine receipts show that customer withdrawals have a skewed distribution with a mean of $72 and a standard deviation of $15.Let Represent the mean withdrawal for the next 200 customers at the machine.Describe the sampling distribution model of this mean.

A 1000-acre farm historically averages 193 bushels per acre with a standard deviation of 16 bushels per acre.Fifty acres are sampled and the mean yield determined.If we imagined all the possible random samples of 50 acres we could take and looked at all the sample means,is it appropriate to assume this data will be well modeled by a Normal distribution?

A candy company claims that 20% of the jelly beans in its spring mix are pink.Suppose that the candies are packaged at random in small bags containing about 200 jelly beans.A class of students opens several bags,counts the various colors of jelly beans,and calculates the proportion that are pink.Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans?

If the students toss the coin 50 times each,about 99.7% should have proportions between what two numbers?

A candy company claims that 9% of the jelly beans in its spring mix are pink.Suppose that the candies are packaged at random in small bags containing about 50 jelly beans.A class of students opens several bags,counts the various colors of jelly beans,and calculates the proportion that are pink.Is it appropriate to use a Normal model to describe the distribution of the proportion of pink jelly beans?

If we imagine all the possible random samples of 250 students at this university,68% of the samples should have means between what two numbers?