The p.d.f. of a random variable X is f(x)=2x for 0

Have American males (AMs) gotten heavier over the last 20 years? A random sample 77 AMs in 2019 had a mean weight of x = 189.030 pounds. A random sample 93 AMs in 1999 had a mean weight of y = 184.795 pounds. It is recognized that the true standard deviation of 2019 AMs weights is σx = 14.04 pounds while it is recognized that the true standard deviation of 1999 AMs weights is σy = 10.03 pounds. The true (unknown) mean of 2019 AMs weights is μx pounds, while the true (unknown) mean of 1999 AMs weights is μy pounds. Weights are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation 2019 Data (X) 77 189.030 14.04 1999 Data (Y) 93 184.795 10.03 i) If we used this data to test H0:μx-μy=0 against the alternative Ha:μx-μy>0 then what would the p value have been? j)If we used this data to test H0:μx-μy=0 against the alternative Ha:μx-μy≠0 then what would the p value have been?

X is the number of red marbles that Suzan has in her hand after she selects 5 marbles from a bag containing 5 red marbles and 2 green ones. expected value       variance       standard deviation

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

Times for a procedure are normally distributed. There are 2 methods. Method A has a mean of 25 minutes and  a standard deviation of 8 minutes. Method B has a mean of 29 minutes and a standard deviation of 4 minutes. Which procedure is preferred if it must be completed within 33 minutes?

Have American males (AMs) gotten heavier over the last 20 years? A random sample 77 AMs in 2019 had a mean weight of x = 189.030 pounds. A random sample 93 AMs in 1999 had a mean weight of y = 184.795 pounds. It is recognized that the true standard deviation of 2019 AMs weights is σx = 14.04 pounds while it is recognized that the true standard deviation of 1999 AMs weights is σy = 10.03 pounds. The true (unknown) mean of 2019 AMs weights is μx pounds, while the true (unknown) mean of 1999 AMs weights is μy pounds. Weights are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation 2019 Data (X) 77 189.030 14.04 1999 Data (Y) 93 184.795 10.03 d) Calculate the standard deviation of X - Y? . e) If we wish to create an 98% confidence interval for μx-μy then what is the z critical value used? f)Create an 98% confidence interval for μx-μy .

The life of light bulbs is distributed normaly, The variance of the lifetime is 900 and the mean lifetime of a bulb is 550 hours. Find the probablty of abulb lasting forat least 583 hours. Round your anvwer to four decimal places