A continuous random variable X has a normal distribution with mean 12.25. The probability that X takes a value less than 13.00 is 0.82. Use this information and the symmetry of the density function to find the probability that X takes a value greater than 11.50

Given the probability density function f(x) = over the interval [2, 7], find the expected value, the mean, 5 the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation: > Next Question

Suppose the weight of pieces of passenger luggage for domestic airline flights follows a normal distribution with u = 28 pounds and o = 5.5 pounds. (a) Calculate the probability that a piece of luggage weighs less than 32 pounds. (Assume that the minimum weight for a piece of luggage is 0 pounds.) (b) Calculate the weight where the probability density function for the weight of passenger luggage is increasing most rapidly. Ib (c) Use the Empirical Rule to estimate the percentage of bags that weigh more than 17 pounds. (d) Use the Empirical Rule to estimate the percentage of bags that weigh between 22.5 and 39. (e) According to the Empirical Rule, about 84% of bags weigh less than pounds. Submit Answer View Previous Question Question 4 of 7 View Next Question Home My Assignments Request Extension 11:16 AM W) 59°F P Type here to search 10/19/2021 4 BA ins prt sc delete home end f10 12 f3 米 f4 f5 f6 10 fg & num + backspace lock 2 3. 4 6. 7. 00 II %24 %23

A random variable X has density 3x2 for 0 < x < 1. Find its variance.(use a decimal number, rounded to the nearest 1,000th. For example, 0.123)

Use the given probability density function over the indicated interval to find the mean, variance, and standard deviation of the random variable. Then sketch the graph of the density function and locate the mean on the graph.

Students arrive at a lecture theatre independently. Suppose the number of students arriving in an hour follows a Poisson distribution with mean 10. Let 7 (in hours) be the time required to wait for 5 students to arrive. Derive the probability density function of T.

3. Which exponential probability density has mean u = ?

The density function of the continuous random variable X is shown below. When c≈ 0.163, Find: (1) the mode, (2) the median, and (3) the mean. Jcsin (2 -0.2x) for 1≤ x ≤ 10 f(x) = {0 elsewhere mahamdy@uoanbar.edu.iq