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1. (16 points) Assume that you toss a fair coin 5 times.(a) (6 pts) What is the probability that you get 5 heads? (Show work and write theanswer in simplest fraction form)(b) (6 pts) What is the probability of getting heads in the 5 th toss, given that the firstfour tosses are tails? (Show work and write the answer in simplest fraction form)(c) (4 pts) If event A is âGetting heads in the 5th tossâ and event B is âThe first fourtosses are tailsâ. Are event A and event B independent? Please explain.2. (8 points) A high school with 1000 students offers two foreign language courses :French and Japanese. There are 150 students in the French class roster, and 80students in the Japanese class roster. We also know that 30 students enroll in bothcourses. Find the probability that a random selected student takes neither foreignlanguage course. (Show work and write the answer in simplest fraction form)3. (12 points) Imagine you are in a game show. There are 5 prizes hidden on a gameboard with 20 spaces. One prize is worth $500, another is worth $200, and three areworth $50. You have to pay $50 to the host if your choice is not correct. Let therandom variable x be the winning.(a) (4 pts) Complete the following probability distribution. (Show the probability infraction format and explain your work)x-$50$50$200$500P(x)(b) (4 pts) What is your expected winning in this game? (Show work and round theanswer to two decimal places)(c) (4 pts) What is the standard deviation of the probability distribution? (Show workand round the answer to two decimal places)4. (12 points) Mimi just started her tennis class three weeks ago. On average, she isable to return 20% of her opponentâs serves. If her opponent serves 10 times, answerthe following questions:(a) (8 pts) What is the probability that she returns at least 2 of the 10 serves from heropponent? (Show work and round the answer to 4 decimal places)(b) (4 pts) How many serves can she expect to return? (Hint : What is the expectedvalue?) (Show work and round the answer to 2 decimal places)5. (16 points) If the IQ scores are normally distributed with a mean of 100 and astandard deviation of 15.(a) (6 pts) Find the probability that a randomly selected person has an IQ scorebetween 88 and 118. (Show work and round the answer to 4 decimal places)(b) (4 pts) If 100 people are randomly selected, what is the standard deviation of thesample mean IQ score. (Show work and round the answer to 2 decimal places)(c) (6 pts) If 100 people are randomly selected, find the probability that sample meanIQ score is greater than 97. (Show work and round the answer to 4 decimal places)6. (8 points) Menâs heights are normally distributed with mean 69.0 inches andstandard deviation 2.8 inches. Mimi is designing a plane with a height that allows95% of the men to stand straight without bending in the plane. What is the minimumheight of the plane? (Show work and round the answer to 2 decimal places)7. (8 points) There are 10 members in the UMUC Stats Club.(a) (4 pts) The Club must select a president, a vice president and a treasurer for theschool year. How many different ways can the officers be selected? (Show work)(b) (4 pts) The Club is sending a delegate of 2 members to attend the 2015 JointStatistical Meeting in Seattle. How many different ways can the delegate be selected?(Show work)