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[answered] 1. (8 points) Assume that you make random guesses for 5 tru

I need some help with the following attached quiz. Thank you for your time.

1. (8 points) Assume that you make random guesses for 5 true-or-false questions.

(a) (3 pts) What is the probability that you get all 5 answers correct? (Show work and

write the answer in simplest fraction form) (b) (3 pts) What is the probability of getting the correct answer in the 5 th question,

given that the first four answers are all wrong? (Show work and write the answer in

simplest fraction form) (c) (2 pts) If event A is ?Getting the correct answer in the 5 th question? and event B is

?The first four answers are all wrong?. Are event A and event B independent? Please

explain.

2. (4 points) A high school with 1000 students offers two foreign language courses :

French and Japanese. There are 200 students in the French class roster, and 80

students in the Japanese class roster. We also know that 30 students enroll in both

courses. Find the probability that a random selected student takes neither foreign

language course. (Show work and write the answer in simplest fraction form) 3. (6 points) Imagine you are in a game show. There are 4 prizes hidden on a game

board with 16 spaces. One prize is worth $4000, another is worth $1500, and two are

worth $1000. You have to pay $50 to the host if your choice is not correct. Let the

random variable x be the winning.

(a) (2 pts) Complete the following probability distribution. (Show the probability in

fraction format and explain your work)

x P(x)

1 -$50

$1,000

$1,500

$4,000 (b) (2 pts) What is your expected winning in this game? (Show work and round the

answer to two decimal places) (c) (2 pts) What is the standard deviation of the probability distribution? (Show work

and round the answer to two decimal places) 4. (6 points) Mimi just started her tennis class three weeks ago. On average, she is

able to return 15% of her opponent?s serves. If her opponent serves 10 times, answer

the following questions:

(a) (4 pts) What is the probability that she returns at least 2 of the 10 serves from her

opponent? (Show work and round the answer to 4 decimal places) (b) (2 pts) How many serves can she expect to return? (Hint : What is the expected

value?) (Show work and round the answer to 2 decimal places) 2 5. (8 points) If the IQ scores are normally distributed with a mean of 100 and a

standard deviation of 15.

(a) (3 pts) Find the probability that a randomly selected person has an IQ score

between 88 and 115. (Show work and round the answer to 4 decimal places) (b) (2 pts) If 100 people are randomly selected, what is the standard deviation of the

sample mean IQ score. (Show work and round the answer to 2 decimal places) (c) (3 pts) If 100 people are randomly selected, find the probability that their mean IQ

score is greater than 97. (Show work and round the answer to 4 decimal places) 3 6. (4 points) Men?s heights are normally distributed with mean 69.0 inches and

standard deviation 2.8 inches. Mimi is designing a plane with a height that allows

95% of the men to stand straight without bending in the plane. What is the minimum

height of the plane? (Show work and round the answer to 2 decimal places) 7. (4 points) There are 10 members in the UMUC Stats Club.

(a) (2 pts)The Club must select a president, a vice president and a treasurer for the

school year. How many different ways can the officers be selected? (Show work) (b) (2 pts) The Club is sending a delegate of 2 members to attend the 2015 Joint

Statistical Meeting in Seattle. How many different ways can the delegate be selected?

(Show work) 4

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