## Math 3118 Practice Exam 5-1

1. True or False? The standard deviation \sigma cannot be a negative number.

2. Suppose that the weight of adult males in the US is normally distributed with mean 179.6 and standard deviation 31.2. What approximate percentage of adult males weigh less than 150?

3. A 100 question multiple choice test is given. 60 of the questions have 5 choices, and the remaining 40 questions have 4 choices A student does not read the questions, instead she randomly chooses an answer. How many correct answers can she expect to get?

4. Find the mean and the standard deviation of the following set of 5 numbers: {x_1,x_2,x_3,x_4,x_5}, where x_i=\sum_{j=1}^i j.

5. Explain why the following is true: \sum_{k=1}^n (n choose k)=2^n-1.

## Math 3118 Practice Exam 5-2

1. Find the standard deviation and mean of {11,0,-11,8}. Leave your results as fractions, not decimals.

2. True or False? Give your reason. The mean of a list of data must be no greater than the largest number on the list.

3. On the SAT math exam the mean is 512 with standard deviation 78. If my score is 666, what approximate percentage of the examinees are within one standard deviation of my score?

4. A fair coin is flipped 3 times. If 0 heads appears, you get $1, if 1 head appears you get$2, if 2 heads appear you get $4, if 3 heads appear you get$8. What are your expected winnings?

5. Write in summation notation the following theorem: The sum of the first n positive odd integers is the square of n.

## Math 3118 Practice Exam 5-3

1. True or False? Give your reason. For any set of data, the average of the square must be greater than or equal to the square of the average.

2. In a dart game you have a 10% chance of a bullseye. Find the approximate probability that in 1000 throws you will have between 90 and 120 bullseyes.

3. Let a_i=(4 choose i), find \sum_{j=1}^3 a_j*a_{j+1}.

4. Suppose we have a list of 100 numbers whose mean is 0 and whose standard deviation is 1. We now add the numbers {4,-4} to our list. Show that the mean of the new list is still zero, but the new standard deviation is greater than 1. Can you find the new standard deviation?

5. In a dice game I roll two dice. If I get a seven I win $5, if I get eleven I win$15, otherwise I pay $2. What are my expected winnings? ## Math 3118 Practice Exam 5-4 1. Give an example of a set of data of size 4 whose mean is 0 and whose standard deviation is less than 1. 2. A so-called psychic guesses colors of cards (red, blue, or yellow). What is the approximate probability that by randomly guessing he can guess at least 50 correct out of 100 tries? 3. True or False. For the mean of a set of data to be zero, each number in the set must be paired with its negative which is also in the set. 4. You draw a single card from a 52 card deck. I now guess what the card is, for example I may guess queen of hearts. If my guess has the correct suit, you pay me$3, If my guess has the correct rank (queen here) you must pay me $2. So I could win$3, $2, or$5 from you. Otherwise, if my guess is all wrong I pay you \$1. What are my expected winnings?

5. True or False? (\sum_{i=1}^n x_i)^2= \sum_{i=1}^n x_i^2.