(1) y μ = σ = (2) v = 4x μ = σ= x+8 σ= mean and standard deviation of a random variable x are 8 and 1 respectively. Find the mean and standard deviation of the given random variables: (3) w = 4x+8 μ =
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- If a is a hypergeometric random bie, compute the mean the variance, 'he standard deviation and the population coection factorfach the following cases: : (a) N= 8, M = 15, n = 13, r = 1 H = 195/8 o2 = 975/64 population correction factor= (b) N = 7, M = 8, n = 14, x = 7 H= 16 population correction factor= (c) N = 14, M = 15, n = 11, x = 5 population correction factor= (d) N = 10, M = 15, n = 6, x = 5 population correction factor=In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?A population has parameters μ=37μ=37 and σ=54.8σ=54.8. You intend to draw a random sample of size n=209n=209.What is the mean of the distribution of sample means?What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)
- A random sample of 10 observations from population A has sample mean of 152.3 and a sample standard deviation of 1.83. Another random sample of 8 observations from population B has a sample standard deviation of 1.94. Assuming equal variances in those two populations, a 99% confidence interval for μA − μB is (-0.19, 4.99), where μA is the mean in population A and μB is the mean in population B. (a) What is the sample mean of the observations from population B? (b) If we test H0 : μA ≤ μB against Ha : μA > μB, using α = 0.02, what is your conclusion?Suppose that X₁,..., Xn are i.i.d. from a normal population with mean μ and variance o². Calculate the expected value and the variance of the sample mean X and find the distribution of √n(X − µ).X is a normally distributed random variable with a mean of 5 and a standard deviation of 2. For which value of a is P(X > a) = 0.6293? What is a?
- A random sample of size n = 70 is taken from a finite population of size N = 500 with mean μ = 220 and variance σ2 = 324. Calculate the standard error of the sample mean.A sample is selected from a normal population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean an extreme, unrepresentative value for the populationAssume that a random variable Y has a mean of zero and standard deviation of one. Calculate the expected value of X1 and X2 if they are defined as below. X1 = Sigma+ Mu X2 = Sigma(Y+Mu)
- The random variable Z has mean 30 and variance 225. Calculate the limits between which you would expect the bulk of observations to lie for the random variable Z/3 − 7.A sample obtained from a population with σ = 48 has a standard error of σM = 6. How many scores are in the sample?The amount of gasoline in gallons sold by three different gas stations during one day is given by the independent random variables X1,X2, X3 each with a normal distribution. X1 has a mean µl =700 and standard deviation ơ1 55; X2 has mean u2 =700 and standard deviation o2 = 65; X3 has mean u3=900 and standard deviation 03 = 100. Suppose the prices per gallon are $2.90, $3.00 and $3.10 for X1, X2, and X3 respectively. Find the probability that the combined revenue for a given day is less than $6000. Use the z-score table. Round answer to the nearest hundredth.
