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- Suppose that contamination particle size (in microm- eters) can be modeled as f(x)=2x³ for 1 < x. Determine the mean of X. What can you conclude about the variance of X?If Y is Normally distributed , and p(y < 170 ) = 0.14 p ( y > 200 ) = 0.03 then the values of the mean and variance of Y , respectively areLet x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.78? Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: ? < 4.78; H1: ? = 4.78H0: ? = 4.78; H1: ? ≠ 4.78 H0: ? = 4.78; H1: ? < 4.78H0: ? = 4.78; H1: ? > 4.78H0: ? > 4.78; H1: ? = 4.78 (b) What sampling…
- Prove the propertyFresh Mart QQ's profit on each delivery is estimated by RM P, where the random variable P has mean u and variance 1.92. According to previous record, the value of u used to be 0.85. Manager suspects that this value has increased. In order to test at the 5% significance level whether the value of u has increased, a random sample of 50 delivery transaction is chosen. Assume the variance of P is unchanged. Given that Ep 59. Find the unbiased estimates of the population mean. Stating the null and alternative hypotheses, test at 5% significance level on whether the manager's suspicion is true. The alternative hypothesis for a test is stated as below: H:µ # 30 State the null hypothesis and determine whether this test is one-tail test or two- tail test hypothesis.Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…
- For any variable X, if: the standard deviation = and the variance = Var(X) Which of the following statement is true: Select one: a. SD < Var(X) O b. (SD)² = Var(X) (SD) C. SD = [var(x)]²Compute the standard score (Z-score) for x, when x = 21, the mean of the distribution = 27, and the variance (S2) = 9. Z = %3D O 2 -2 .67 -.67Let Y be the life in hours of a battery. Assume Y is normally distributed with mean 200 and variance o?. If a purchaser of such batteries requires that at least 90% of the batteries have lives exceeding 150 hours, what is the largest value o can be and still have the purchaser satisfied?