(a) Find Var(X). (b) Find P(3.39 ≤X ≤ 3.6), approximately. (c) What assumptions have you made?
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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.3. The Central Limit Theorem states that the mean of the sampling distribution of the sample mean is A. larger than the population mean. B. exactly equal to the population mean. C. equal to the population mean divided by the square root of the sample size. D. close to the population means if the sample size is large.
- In a random sample of 320 cars driven at low altitudes, 50 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 135 cars driven at high altitudes, 17 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is less than the proportion of low-altitude vehicles exceeding the standard? Let p1 denote the proportion of low-altitude vehicles exceeding the standard and p2 denote the proportion of high-altitude vehicles exceeding the standard. Use the =α0.10 level of significance and the P -value method with the TI-84 Plus calculator. please state all steps to the p method clearly!A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples? (A) The margin of error for S will be 4 times the margin of error for R. (B) The margin of error for S will be 2 times the margin of error for R. (C) The margin of error for S will be equal to the margin of error for R. (D) The margin of error for R will be 4 times the margin of error for S. (E) The margin of error for R will be 2 times the margin of error for S.Let Yn denote the nth order statistic of a random sample of size n froma distribution of the continuous type. Find the smallest value of n for which theinequality P(ξ0.9 < Yn) ≥ 0.75 is true.
- For any sample of size 120 the population mean, the mean of the sampling distribution for the sample means, and the sample mean will always be equal to each other. True or False When using the central limit theroem for means with n = 68, it is not necessary to assume the distribution of the population data is normally distributed. True or False The symbole op represents the standardIf We can assert with 95% that the maximum error is 0.05 and p= 0.2 ,find the sample size...An analyst is interested in knowing whether the proportion of childless couples in a community deviates significantly from the statewide average of 0.12. The analyst suspects a priori that the proportion of childless couples in her community is higher than the statewide average. A sample of 100 couples is interviewed; the mean proportion of childless couples in the sample is found to be 0.16. Test the null hypothesis that the ‘true’ proportion could be 0.12 and give the p-value. Use α = 0.06.
- Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributedSuppose that X has a Poisson distribution with h = 80. Find theprobability P(x is less than or equal to 80)Let X1 and X2 be observations of a random sample of size n = 2 from a Cauchy Distribution.Find P(X1 < −1 and 1 < X2)
