Work out the following problems and show all necessary steps to earn full credit.

1. Tallest and Shortest Men The tallest living man at the time of this writing is Sultan Kosen, who has a height of 251 cm. The shortest living man is Chandra Bahadur Dangi, who has a height of 54.6 cm. Heights of men have a mean of 174.12 cm and a standard deviation of 7.10 cm. Which of these two men has the height that is extreme? (4 points)

2. Assume that random guesses are made for ten multiple-choice questions on an SAT test, so there is n=10 trials, each with probability of success (correct) gives by p= 0.2. That means each question has 5 choices with only one appropriate answer. Find the indicated probability for the number of correct answers.

a. Is this a binomial Experiment? Why? (4 points)

b. Find the probability that the number of correct answers/guesses is exactly 6 (Use the binomial formula first then StatCrunch) (4 points)

c) Find the probability that the number of correct answers/guesses is at least 9. Is the outcome 9 significantly high? Why? (4 Points) (Use the binomial formula first then StatCrunch)

d) Find the probability that the number of correct answers/guesses is at most 1 (no more than 1). Is the outcome 1 significantly low? Why? (4 Points) (Use the binomial formula first then StatCrunch)

e) Find the probability that the number of correct answers/guesses is no correct answer(none). (4 Points) (Use the binomial formula first then StatCrunch)

f) Find the mean and the standard deviation of the random variable X (# of correct guesses) and interpret their meaning. [Use formula] (4 Points)

3. Scores on the Wechsler Adult intelligence Scale (a Standard IQ test) for certain age group are normally distributed with mean = 100 and standard deviation = 15. (Find the Z score/s for each question first, and then use Table A-2 at the back of your book to find the following probabilities)

a. What percent of IQ scores are less than 122? (4 points)

b. What is the probability that a randomly selected adult in this age group has an IQ score higher than 147? Is this a significant/unusual event? Explain? (5 points)

c. What percent of adults in this age group have IQs between 85 and 100? Is this significant/unusual event? Explain? (5 points)

d. MENSA is an elite organization that admits as members' people who score in the top 2% on IQ tests. What score on the Wechsler Adult Intelligence Scale would an individual have to earn to qualify for MENSA membership? (4 points)

e. Find the first quartile (Q1)? Hint: (Q1 separates the bottom 25%) (4 points)