Given that μ = 12 and σ = 4 . Suppose samples of size five are taken. What is the mean of the sampling distribution? What is the standard deviation of the sampling distribution?
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Given that μ = 12 and σ = 4 . Suppose samples of size five are taken.
- What is the mean of the sampling distribution?
- What is the standard deviation of the sampling distribution?
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- A population has a mean of 60 and a standard deviation of 5. A random sample of 16 measurements is drawn from this population. Describe the sampling distribution of the sample means by computing its mean and standard deviation. Assuming that the population is infinite. 1. What is the mean of sampling distribution? 2. What is the standard deviation of the sampling distribution?Suppose x has a normal distribution with mean ? = 53 and standard deviation ? = 7.Describe the distribution of x values for sample size n = 4. (Round ?x to two decimal places.) ?x = ?x = Describe the distribution of x values for sample size n = 16. (Round ?x to two decimal places.) ?x = ?x = Describe the distribution of x values for sample size n = 100. (Round ?x to two decimal places.) ?x = ?x =This assignment is worth 1 points. The extra point will be added to your overall course grade. For example: if you receive an 88% in the course you can receive up to 1 point giving you a new score of 89%. The following rubric will be used. 0.25 point for drawing the normal distribution curve with the mean value labeled on the curve and the appropriate area shaded. 0.25 point for determining the value of the standard deviation of the sample mean. 0.5 point for finding the correct probability. All work must be shown in order to receive any credit. Please upload your completed assignment here. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.
- Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is $229 with a standard deviation of $63. Random samples of size 24 are drawn from this population and the mean of each sample is determined. The mean of the distribution of sample means isThe distribution of the number of motor vehicles per household in the United States (the population) and sampling distributions of the mean for samples of size 4 and 10 are shown in below. A.Which distribution is which? Make a rough estimate of the mean and standard deviation of each distribution. Explain the reasons of your choices.b. The mean of the population is about 1.7. Theoretically, what is the mean of the sampling distribution for samples of size 4? Of size 10? Are these computed means consistent with your estimates of the means in the histograms? Briefly explain.c. The standard deviation of the population is about 1. Theoretically, what is the Standard Error (SE) of the sampling distribution for samples of size 4? Of size 10? Are these computed SEs consistent with your estimates of the SEs in the histograms? Briefly explain.d. Compare the shapes of the three distributions. Are the shapes consistent with the Central Limit Theorem? Briefly explain.A population has a mean p= 75 and a standard deviation o= 6. Find the mean and standard deviation of a sampling distribution of sample means with sample size n= 36. (Simplify your answer.)
- What is the mean and standard deviation of the sampling distribution of X¯X¯ for n = 16, if the sampled population has a mean of 48 and a standard deviation of 12? Select one: a. 4 and 1 b. 12 and 3 c. 48 and 3 d. 48 and 1 e. 48 and 12Suppose that the average number of sick days that a person at the company takes per year is 3.2 with a standard deviation of .75. You select a sample of 125 employees. a. Is the sampling distribution for the mean of the sick days for 125 employees normally distributed? Explain how you know in complete sentences and be specific. b. What is the mean and standard deviation for the sampling distribution for the mean of 125 employees sick days? Show your work and calculations. c. Suppose that a group of 125 employees has a mean of 3.7 days. What is the probability that a group of 125 employees would take more sick days than them? You should use technology to find this value and write the probability notation. d. Suppose that a group of 35 employees has a mean of 3.5 days. Would that group have taken an unusual number of sick days?The first experiment I created 200 samples with 10 students in each and took each sample's mean. The mean of this distribution was about 10.7 miles with a standard deviation of 3.7 miles. (See video) Next I did 200 samples with 20 students each, then I did 200 samples with 50 students each and finally I did 200 samples with 100 students each. Watch the following video and answer the following questions about the sampling distributions being created. 1) For the samples with 100 students each, when the sampling is complete, what will the mean be close to or equal to? 2) For the samples with 100 students each, when the sampling is complete, will the standard deviation be smaller than the standard deviation for the samples with 50 students each? 3) What is the mean of the population of students that I am randomly sampling from? 4) What is the name of the important theorem that I am demonstrating right now.?
- If we meet these conditions, the sampling distribution of the mean will have a normal shape and ... The mean of the sampling distribution will be u, (i.e., the same as the population mean) and the standard deviation of the sampling distribution will be (that's the population standard deviation divided by the square root of the sample size). In the AP Stats Guy video, he talks about the number of text messages his students send during class. Suppose the average number of text messages his students send during class is u = 30 text messages. If we take samples of say, n = 36 students at a time, we would expect the mean of the sampling distribution we create to be the same as the population mean, 30 text messages. If we can further say that standard deviation of the number of text messages is 12 text messages, by how much would we expect the sample means to vary? (hint, use the formula above) text messagesSuppose the mean blood pressure for people in a certain country is 130 mmHg with a standard deviation of 24 mmHg. Blood pressure is normally distributed. State the random variable. The mean blood pressure of people in the country. The standard deviation of blood pressures of people in the country. O The blood pressure of a person in the country. Suppose a sample of size 10 is taken. State the shape of the distribution of the sample mean. The shape of the sampling distribution of the sample mean is unknown since the population of the random variable is normally distributed and the sample size is less than 30. The sampling distribution of the sample mean is normally distributed since the population is normally distributed. The sampling distribution of the sample mean is unknown since the sample size is less than 30. Suppose a sample of size 10 is taken. State the mean of the sample mean. Suppose a sample of size 10 is taken. State the standard deviation of the sample mean. Round to two…A population has a mean u = 157 and a standard deviation o = 20. Find the mean and standard deviation of the sampling distribution of sample means with sample size n= 43. The mean is and the standard deviation is o; = (Round to three decimal places as needed.)