Suppose that a new treatment is successful in curing a common ailment 61% of the time. If the treatment is tried on a random sample of 105 patients, approximate the probability that more than 67 will be cured. Use the normal approximation to the binomial with a correction for continuity.

Find the probability that a normal variable takes on values more than  1 6  standard deviations away from its mean.

Please use excel formulas when possible:   You have a device that uses a single battery, and you operate this device continuously, never turning it off. Whenever a battery fails, you replace it with a brand new one immediately. Suppose the lifetime of a typical batteryhas an exponential distribution with mean 205 minutes. Suppose you operate the device continuously for three days, making battery changes when necessary. Find the probability that you will observe at least 25 failures. (Hint: The number of failures is Poisson distributed.) In the previous problem, we ran the experiment for a certain number of days and then asked about the number of failures. In this problem, we take a different point of view. Suppose you operate the device, starting with a new battery, until you have observed 25 battery failures. What is the probability that at least 15 of these 25 batteries lived at least 3.5 hours? (Hint: Each lifetime is exponentially distributed

Use the formula to find the standard error of the distribution of differences in sample means, x⎯⎯1−x⎯⎯2x¯1-x¯2.Samples of size 40 from Population 1 with mean 3.7 and standard deviation 1.9 and samples of size 40 from Population 2 with mean 1.9 and standard deviation 1.2Round your answer for the standard error to two decimal places.standard error = Enter your answer in accordance to the question statement