i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal random variable. ind What in 5033
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- Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with u 90.3 ft and o 68.8 ft. You intend to measure a random sample of n = 87 trees. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)? (Report answer accurate to 2 decimal places.) Check AnswerWhat does a standard z-value mean?a. it expresses distance from the mean in units of the standard deviation.b. it provides a positive value for a random variable Xc. it provides a negative value for a random variable Xd. all of the aboveThe article "Uncertainty Estimation in Railway Track Life-Cycle Cost"t presented the following data on time to repair (min) a rail break in the high rail on a curved track of a certain railway line. 159 120 480 149 270 547 340 43 228 202 240 218 n USE SALT A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population distribution of repair time is at least approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. (a) Is there compelling evidence for concluding that true average repair time exceeds 200 min? Cary out a test of hypotheses using a significance level of 0.05. State the appropriate hypotheses. Ο H: μ= 200 Hai u > 200 Но: и 200 Ha: u = 200 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) t = P-value = What can you conclude? There is compelling evidence that the true average repair time…
- The population mean and standard deviation of a normally distributed random variable is 3.5 and 2.12 respectively. Find the z score for x = 4.1? Round answer to 2 decimalsAssume that adults have IQ scores that are normally distributed with a mean of m = 105 and a standard deviation s =15. Find the probability that a randomly selected adult has an IQ between 91 and 119. The probability that a randomly selected adult has an IQ between 91 and 119 is ____.B.202 ul X с Too Weekly w sal Success C X Bb Exam 2 X Bb Take Test: Bb UTF-8 Ass Question Completion Status: nccu.blackboard.com/webapps/assessment/take/launch.jsp?course_assessment_id=_26 http: QUESTION 8 For any continuous random variable, the probability that the random variable takes a value less than zero a. is any number between zero and one. b. is more than one, since it is continuous. c. is a value larger than zero. d. is zero. QUESTION 9 For the standard normal probability distribution, the area to the right of the mean is a. 1. b. 3.09.
- An urn contains 7 black and 18 white balls. A ball is randomly drawn from the urn. Let X = 1 if a white ball is drawn and let X = -1 if a black ball is drawn. Find the following a) mean of X b) variance of X Please provide your working and round your answers to 2 decimal placesExecutives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, u, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate u. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 99% confident that her estimate is within 5 minutes of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) ?In a sporting event, the championship is won by the first team to win four games. The lengths of the championship games are given in the table. Let X denote the number of games that it takes to complete a championship, and Y denote the number of games that it took to complete a randomly selected championship from among those considered in the table. a. Determine the mean and standard deviation of the random variable Y. The mean is games. (Round to three decimal places as needed.) The standard deviation isgames. (Round to three decimal places as needed.) Number of games Frequency Relative Frequency 4 22 0.196 5 27 0.241 6 27 0.241 7 36 0.321
- Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 6.5752 7.3865 is the standard deviation of the second sample.A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. State the conclusion for the test. Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women. μ n X S Men 11 11 97.53°F 0.76°F Women H₂ 59 97.46°F 0.69°F O A. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. OB. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women. OC. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. OD. Reject the null hypothesis. There is sufficient evidence to support the claim…A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. State the conclusion for the test. Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women. μ n X S Men H₁ 11 97.66°F 0.75°F Women H₂ 59 97.22°F 0.68°F O A. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. O B. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. O C. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women. O D. Fail to reject the null hypothesis. There is sufficient evidence to support the…