A binomial random variable X reveals pµ=100 and o=20. Calculate P{X>101}.
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- 8% of all cars fail the emissions inspection, find the probability that in a sample of 85 cars, 11 will fail. Use the Poisson approximation to Find the mean number λ of cars that fail the emissions inspection in a sample of 85 cars.Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. A. What is the variance of the sample mean Xn? B. Use your answer to part (A), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that sample mean Xn is more than a certain distance of 175A Binomial experiment has 100 trials and a probability of success of 0.8.Determine the mean of this experiment.
- 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?If continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75 <= x <= 300.35) ?If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? Explain
- Assume 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.We have a random variable X1 for population 1 with a mean value of 52 and standard deviation of 3. we have a random variable X2 for population 2 with a mean value of 50 and population standard deviation of 4. we obtain a random sample of 625 elements independently for both populations. what is the probability that the difference in the sample averages X1-X2 is at least 2.3?
