The number of dirt specks on a randomly selected square yard of polyethylene film of a certain type has a Possion distribution with a mean value of 2 specks per square yard. Consider a random sample of n = 5 film specimens, each having area 1 square yard, and let X be the resulting sample mean number of dirt specks. Obtain the first 21 probabilities in the X sampling distribution. [Hint: What does a moment generating function argument say about the distribution of X1+ …+ X;?]

Recall that Benford's Law clalms that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a v leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millons of numbers in a large computer data bank. You draw a random sample of n = 229 numbers from this file and r 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. large data file, the probability of getting a number with "1" as the () Test the dalm that p is more than 0.301. Use a 0.10. (a) what is the level of signifcance? State the null and alternate hypotheses. O Hg: p = 0.301; H p> 0.301 O Hgi P = 0.301; Hip 0.301; Hp- 0.301 O Ho: P= 0.301; H: p- 0.301 (b) what sampling distribution will you use? O The Student's t, since np > 5 and ng > 5. O The…

Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with a = 2.6, B = 1.8, and y = 0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in the equation below, :- le-(x/B)a pa a x 2 0 f(x; а, B) %3D x 1.5). (Round your answer to four decimal places.) 0.8050 (c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.) 1.878 X days (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) mean days standard deviation days