The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 502 psi. I USE SALT (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,900 and 10,200? (Round your answer to four decimal places.) (b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning. ○ Yes, the probability in part (a) can still be calculated from the given information. O No, n should be greater than 30 in order to apply the Central Limit Theorem. O No, n should be greater than 20 in order to apply the Central Limit Theorem. ○ No, n should be greater than 50 in order to apply the Central Limit Theorem.

3. Determine the following from the graph. Show all your work. a. Determine the mean and standard deviation: PDF of a Random Variable ū 6.09 COM 0.04 · b) Draw a qualitative sketch of the CDF of the distribution shown. Be sure to show axis values and key values that are appropriate! 0 10 c) What type of distribution was the PDF of a Random Variable?

A variable of a population has a mean of µ = 82 and a standard deviation of o = 9. a. Identify the sampling distribution of the sample mean for samples of size 81. b. In answering part (a), what assumptions did you make about the distribution of the variable? c. Can you answer part (a) if the sample size is 25 instead of 81? Why or why not? a. What is the shape of the sampling distribution? normal uniform skewed O bimodal What is the mean of the sampling distribution? Hi = (Simplify your answer.) What is the standard deviation of the sampling distribution? (Simplify your answer.) b. In answering part (a), what assumptions did you make about the distribution of the variable? A. It was assumed that the variable was normally distributed. B. No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideratio

': Consider a puzzle is created where the amount of time it takes an individual to solve the puzzle follows a normal distribution with a standard deviation of 2 minutes. a) If a sample of 13 individuals was collected, what is the probability the sample mean time required to solve the puzzle would be within 1.2 minutes of the population mean? b) What would the required sample size be if we wanted the sample mean to be within half a minute of the population mean with a probability of .9?

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.7 ppm and standard deviation 1.7 ppm. 18 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. What is the distribution of T? I - N( c. What is the probability that one randomly selected city's waterway will have more than 8.9 ppm pollutants?

a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three men.   The mean of the sample mean is μx=1.401.40kg. ​(Type an integer or a decimal. Do not​ round.) The standard deviation of the sample mean is σx=0.06350.063kg. ​(Round to four decimal places as​ needed.) Interpret these answers in context.   For samples of three men, the individual brain weights have a normal distribution with a mean of 1.41.4 kg and a standard deviation of  0.06350.0635 kg. ​(Type integers or decimals rounded to four decimal places as​ needed.)

If someone could help me answer this that would be great.