1. What is a random variable? What is the difference between a discrete random variable (RV) and a continuous random variable?For each of the following random variable X, determine whether it is a discrete RVor acontinuous RV. Explain your answer:

a)Flip a coin threetimes. Let X be the total number of heads.

b) Randomly select a student who took a true/false test with 100 questions. Let X be the number of questions answered correctly.

c) Randomly select a mutual fund. Let X be the number of companies in the portfolio.

d) Randomly select 50 community college students. Let X be the exact average age of the group.

e) Randomly select a newborn baby. Let X be the exact length in inches.

2. Answer ONE of the following questions:

• Explain what "success" means in a binomial probability. How the value of p, the probability of success, affects the shape of the binomial probability histogram.
• Explain how the value of n, the number of trials in a binomial experiment, affects the shape of the binomial probability histogram.

3.When we refer to a "normal" distribution, does the word normal have the same meaning as in ordinary language, or does it have a special meaning in statistics? What exactly is a normal distribution?

4. What is the difference between a standard normal distribution and a nonstandard normal distribution?

5. The scores on exam 1 were approximately normal with mean of 78 and standard deviation of 7.

a) What is the probability that a randomly selected student scored between

• 71 and 85?
• 64 and 92?
• 57 and 99?

b) What was the range of scores for the middle:

• 68%?
• 95%?
• 99.7%?

c) Name a rule that you learned in chapter 3 which described the relationship between parts a) and b). Explain your answer.

6. Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to measure the same aptitude. If someone gets an SAT score that is in the 95th percentile, find the actual SAT score and the equivalent ACT score.