1. Innocent until proven guilty? In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. (Source: The Book of Risks, by Larry Laudan, John Wiley and Sons) Suppose you are a news reporter followingfivecriminal trials. (For each answer, enter a number.)(a)If the trials were in Japan, what is the probability that all the defendants would be found guilty? (Round your answer to three decimal places.)What is this probability if the trials were in the United States? (Round your answer to three decimal places.)(b)Of thefivetrials, what is the expected number of guilty verdicts in Japan? (Round your answer to two decimal places.)verdictsWhat is the expected number in the United Sates? (Round your answer to two decimal places.)verdictsWhat is the standard deviation in Japan? (Round your answer to two decimal places.)verdictsWhat is the standard deviation in the United States? (Round your answer to two decimal places.)verdicts2. On the leeward side of the island of Oahu, in a small village, about83%of the residents are of Hawaiian ancestry. Letn= 1, 2, 3, represent the number of people you must meet until you encounter thefirstperson of Hawaiian ancestry in the village.(a)Write out a formula for the probability distribution of the random variablen. (Enter a mathematical expression.)P(n) =3. The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample ofsixsyringes taken from the batch. Suppose the batch contains1%defectivesyringes.(c)What is the probability that the batch will be accepted? (Enter a number. Round your answer to three decimal places.)(d)Find (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.) =syringes4. Suppose approximately75%of all marketing personnel are extroverts, whereas about60%of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.)In a group of5computer programmers, what is the probability that none are introverts?What is the probability that3or more are introverts?What is the probability that all are introverts?5. What is the income distribution of super shoppers? Asupermarket super shopperis defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.Income range5-1515-2525-3535-4545-5555 or moreMidpointx102030405060Percent of super shoppers22%13%21%17%18%9%(c)Compute the expected income of a super shopper (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) =thousands of dollars(d)Compute the standard deviation for the income of super shoppers (in thousands of dollars). (Enter a number. Round your answer to two decimal places.) =thousands of dollarsfile is for number 5.