Central limit theorem for population
Sample sizes of 50 are selected from a normal population with a mean of 78.1 and standard deviation of 16.2. Calculate the probability that a single value selected at random will be between 71.1 and 85.1
Sample sizes of 50 are selected from a normal population with a mean of 78.1 and standard deviation of 16.2. Calculate the probability that a single value selected at random will be between 71.1 and 85.1
The Central Limit Theorem The Sony Corporation produces a Walkman that requires two AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of their testing program
Sampling Distribution and the Central Limit Theorem Find the probabilities. a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 92 inches and a standard deviation ? of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the
A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to est
The amount of time a bank teller spends with each customer has a population mean = 3.1 minutes and population standard deviation = 0.4 minute. a) What is the probability that for a randomly selected customer the service time would exceed 3 minutes? b) If many samples of 64 were selected, what are mean and standard error of t
This question is asking for speculation about the possible results of a study if we change the size of the population. It all depends on unknowns such as how representative the 100 adults are of the population. In general, the larger the population the sure we are that it is representative of the population. In a poll of 1
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000. a. If we select a random sample of 50 households, what is the standard error of the mean? b.
1) A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled "3 pounds". Of course he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds. A) Wh
A new machine has just been installed to cut and rough-shape large slugs. The slugs are then transferred to a precision grinder. One of the critical measurements is the outside diameter. The quality control inspector randomly selected five slugs each hour, measured the outside diameter, and recorded the results. The measurements
(Please see the attachment) "Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000. " "a. If we select a random sample of 50 hou
(a) List four rules for detecting abnormal (special cause) observations in a control chart. (b) Set up a control limits for an x=400, R=5, and n = 4. (Please see the attached document for proper formatting)
The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a. What is the likelihood the sample mean is at least $25.00? b
Visit the following Web site Central Limit Theorem Applet and read what is posted: http://www.stat.sc.edu/~west/javahtml/CLT.html You will choose from the pull down menu at the bottom of the page both the number of dice and the number of rolls at a time. When you "click" you will be virtually rolling your dice. Complete t
Why is the Central Limit Theorem so important to the study of sampling distributions? a. it allows us to disregard the size of the sample selected when the population is not normal b. it allows us to disregard the shape of the samplign distribution when the size of the population is large. c. it allows us to disregard the s
4. A computer supply house receives a large shipment of floppy disks each week. Past experience has shown that the number of flaws per disk can be described by the following probability distribution: Number of Flaws per Floppy Disk Probability 0 .65 1 .2 2
Assume that men's weights are normally distributed with a mean of 172 lbs. and a standard deviation of 29 lbs. I understand that if one man is selected the probability his weight is less than 182 lbs is .6331 However I don't understand if 25 men are randomly selected what is the probability that they have a mean weight les
A population is normally distributed, with a mean of 23.45 and a standard deviation of 3.8. What is the probability of each of the following? a) Taking a sample of size 10 and obtaining a sample mean of 22 or more b) Taking a sample of size 4 and getting a sample mean of more than 26.
What are the main characteristics/points of the Central Limit Theorem for a mean?
Question 1: As a sample size approaches infinity, how does the student's t distribution compare to the normal z distribution? When a researcher draws a sample from a normal distribution, what can one conclude about the sample distribution? Explain. Question 2: A mayoral election race is tightly contested. In a random sam
A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central limit theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population?
1. State the main points of the Central Limit Theorem for a mean. 2. Why is population shape of concern when estimating a mean? What does sample size have to do with it? 3. A random sample of 10 Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were ... [See the atac
Question: Why is population shape of concern when estimating a mean? What does sample size have to do with it? Scenario 1: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were as given below: 3.087 3.131 3.241 3.241 3.270 3.353 3.4
Question 5 State the main points of the Central Limit Theorem for a mean. Question 6 Why is population shape of concern when estimating a mean? What does sample size have to do with it? 8.46 A random sample of 10 Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams we
#1 Answer the following based upon the implications of the Central Limit Theorem (assume sample size larger than 30 when samples are mentioned in (a) and (b) below). a) How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population? b) How does the stan
2) Let X1, X2,... be i.i.d. random variables all having a Gamma distribution with parameters α and 3. Let n = (1/n) ∑i=1nXi. Define h(x) = √(2x). 1) Find the 0.5 quantile of the approximate distribution of n using the central limit theorem. You must show all steps. 2) Find the approximate distribution of h( n) using
What roles does Central Limit Theorum play in evaluations of the confidence level or hypothesis testing?
A. The length of time a person spends waiting in a physician's office for an appointment can be a frustrating experience. The results below are the responses of internists from two multispecialty group practices to the following question: "When patients arrive for midmorning or midafternoon appointments, how long do they g
? Visit the following Web site Central Limit Theorem Applet and read what is posted: http://www.stat.sc.edu/~west/javahtml/CLT.html ? From the pull down menu at the bottom of the page, choose 5 for number of dice. For the number of rolls at a time from that menu, again choose 5. ? Click to roll your virtual dice. Keep trac
What is the sampling distribution of sample means? What is the mean of the sampling distribution of sample means? What is its standard deviation? How is that standard deviation affected by the sample size? What does the central limit theorem state about that distribution?
The mean weight of newborn babies in a Long Island Community is 7.5 lbs with a standard deviation of 1.4 lbs. What is the probability that a random sample of 49 babies has a sample mean weight of at least 7.2lbs?