Practice Exam #2 34. Find the standard deviation of the number of cutthroat trou

Question

Practice Exam #2 34. Find the standard deviation of the number of cutthroat trout that a person 6-hou r period. will catch in a 34 (3 points) ·Show work For questions 35 through 38, use the following information: opping mall, security catches an average of 0.37 incidents of shoplifting every hour. Assume that shoplifting incident catches occur independently of each other Find the expected number of incidents of shoplifting caught be security during a 10-hour period. Show work unless the answer can be read directly from the problem 35_ 36. Find the standard deviation of the number of incidents of shoplifting caught be security during a 10-hour period. Round your answer to one decimal place. *Show work 37. What is the probability that security at the shopping mall will catch 2 incidents of .37 shoplifting during any given 10 3 points) "Show work by implementing the appropriate formula evaluated for each of its factors 38. What is the probability that security at the shopping mall will catch more than 3 incidents 38. of shoplifting during any given 10-hour period? (3 points) Show work by displaying the appropriate probability interval and then using a table to evaluate For questions "39 through *42, use the following information: A research team at Cornell University conducted a study showing that approximately 10% of businessmen who wear neckties wear them so tightly that they actually reduce blood flow to the brain. Suppose that 20 businessmen who wear neckties are selected at random. 39 What is the expected number of businessmen whose neckties are worn too tightly? *39. Show work unless the answer can be read directly from the problem 40. What is the standard deviation of the number of businessmen whose neckties are worn too 4 tightly? Round your answe Show work

Explanation / Answer

Let X be the number of incidents happens in a hour.

It is given that the average number of incidents is 0.37

So here X is poisson random variable with parameter l=0.37

By definition of poisson random variable it is known that E(X) =0.37=var(X)

35) so in 10hours average is 10*E(X)=3.7

36) now Variance of 10 hour is

10*Var(X)=10*.37=37

Hence standard deviation is sqrt(3. 7)=1.92

Now define Y as security caught number of incidents in 10 hours

So Y having poison distribution with parameters lm=10*.37=3.7

Now to find P(Y=2)=exp(-lm)((lm)^2)/2=0.1692

Again to find P(Y=3)=exp(-lm)((lm)^3)/6=0.2087

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