Random variable x has a uniform distribution defined by the probability density function below. 1/100 for values of x between 200 and 300 f(x) = 0 elsewhere else 21. Determine the probability that x has a value between 225 and 250. 22. Determine the probability that x has a value of at least 220. 23. Determine the mean (expected value) of x. 24. Determine the standard deviation of the random variable.25. For a normal distribution, find the area between the mean and a point 1.64 standard deviations to the left of the mean. 26. For a standard normal distribution, find the area between z = -.67 and z = +.15. 27. For a standard normal distribution, determine that probability that z is between 0 and 1.48; that is, find P(0 2.6).North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution. The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels. According to this distribution: 29. How likely is it that NDM's production will be less than 4.5 million barrels? 30. How likely is it that NDM's production will be between 4.8 and 6.0 million barrels? 31. According to this distribution, there is a .005 probability that NDM's production will be greater than how many millions of barrels? 32. How likely is it that NDM's production will be between 5.5 and 6.5 million barrelsThe waiting time before a caller is able to speak to a customer service representative at Chase Bank is exponentially distributed, with an average waiting time of 2.5 minutes 33. How likely is it that a customer will wait at least 3 minutes? 34. How likely is it that a caller will wait less than 2 minutes? 35. How likely is it that a caller will wait between 4 and 5 minutes? Births in the US occur at an average rate of 7.5 births per minute (Source: Censusgov, 2013). Assume all the Poisson conditions are met. 36. What is the expected time (in minutes) between one birth and the next? 37. What is the standard deviation (in minutes) of the \"time between births" random variable