Prove that for any discrete distribution standard deviation is not less than mean deviation from теаn:
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- The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 15 days. Let X be the length of a randomly recorded pregnancy in the village. What is the distribution of X? X ~ N (,) Please show the following answers to 4 decimal places. If a pregnancy randomly chosen in the village, find the probability that it lasted less than 244 days. If a pregnancy randomly chosen in the village, find the probability that it lasted between 290 and 298 days. Please show the following answer to a whole day. The 72nd percentile pregnancy length in this village is ___________ days.Assume that the error term u is normally distributed with a mean of 0 and a standard deviation of 10. What is the value ofSuppose that X~N(5000,400). You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is Normally distributed with a mean of 5000. If you took a sample of size n = 100, what is the standard deviation of that sample?
- 2) From the records of XYZ University, there were 1564 freshmen students who took the IQ test during 1t Sem of S.Y. 2018 – 2019. Assume that the IQ test scores are normally distributed with a mean of 108 and a standard deviation of 12. How many students have IQ scores (a) below 100; (b) above 120; and (c) betwe 95 and 125?Suppose that a researcher is interested in estimating the mean systolic blood pressure, u, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate u. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 26 mm Hg, what is the minimum sample size needed for the researcher to be 99% confident that his estimate is within 4 mm Hg 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.)True or False 4) The standard deviation describes the differences between x. 5) Keep other factors constant, the standard error with a sample size of 50 islarger than the standard error with a sample size of 100. 6) Keeping other factors constant, the 90% CI has a broader range with a samplesize of 50 than with a sample size of 100. 7) Keeping other factors constant, the 99% CI has a broader range than the 95% CI.
- Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 200 people. The sample mean is 22.3 hours. There is a known population standard deviation of 7.0 hours. The population distribution is assumed to be normal. Which distribution should you use for this problem? (Round your answers to two decimal places.) X ~ ,Suppose that a researcher is interested in estimating the mean systolic blood pressure, μ, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate μ. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 26mm Hg, what is the minimum sample size needed for the researcher to be 95% confident that his estimate is within 5mm Hg of μ? 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).Suppose that X~N(5000,400). You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is Normally distributed with a mean of 5000. If you took a sample of size n = 10000, what is the standard deviation of that sample?
- For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 31 beats per minute, the mean of the listed pulse rates is `x=79.0 beats per minute, and their standard deviation is s=14.7 beats per minute. a. What is the difference between the pulse rate of 31 beats per minute and the mean pulse rate of the females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the pulse rate of 31 beats per minutes to a z score. d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 31 beats per minute significant?The mean height of 15 to 18-year-old males from Chile from 2009 to 2010 was 170 cm with a standard deviation of 6.28 cm. Male heights are known to follow a normal distribution. Let X = the height of a 15 to 18-year-old male from Chile in 2009 to 2010. Then X ~ N(170, 6.28). Suppose that the height of a 15 to 18-year-old male from Chile from 2009 to 2010 has a z-score of z = –2. What is the male’s height? (to the nearest hundredths). The z-score (z = –2) tells you that the male’s height is? standard deviations to the (right or left) of the mean?1/ The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 2 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. What is the median recovery time? daysc. What is the Z-score for a patient that took 5.1 days to recover? d. What is the probability of spending more than 4.8 days in recovery? e. What is the probability of spending between 3.5 and 4.1 days in recovery? f. The 90th percentile for recovery times is days. 2/The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 79 minutes and a standard deviation of 15 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the…