Supplemental Instruction
Iowa State University / Leader: / Luyun
Course: / Stat 226
Instructor:
Date: / 1/31/16
True/False Quiz
For questions 1-15, answer true or false. If the statement is false, change it in a way that makes it true. Try to complete this quiz on your own without using your notes.
____ 1.) A statistical model is a breakdown of variation into a predictable pattern and the
remaining variation.
____ 2.) Adding the probabilities associated with all outcomes of a random event yields 1.
____ 3.) Statistical models are only adequate if they predict reality exactly.
____ 4.) A random variable describes the probabilities for an uncertain, past numerical outcome
of a random process.
____ 5.) A random variable that takes on any value in an interval is called a discrete random
variable.
____ 6.) The Probability Distribution of a Random Variable is a function that assigns
probabilities to each possible outcome of the random variable.
____ 7.) The area under any density curve is always equal to 1.
____ 8.) Every normally distributed random variable follows a probability distribution that is
characterized by the mean µ and the variance σ2.
____ 9.) The larger the σ2, the less variability in our data.
____ 10.) To denote that a variable follows a normal distribution, we use X~N(µ,σ2).
____ 11.) The normal distribution is symmetric about its variance σ2.
____ 12.) The 68-95-99.7 Rule, also known as the Empirical Rule, says that approximately 68%
of the data in a normal distribution fall within a range of (µ-2σ, µ+2σ).
____ 13.) 13.5% of the data in a normal distribution will be between µ+σ and µ+2σ, according to
the Empirical Rule.
____ 14.) The standard normal distribution has a mean of 0 and a variance equal to 1.
____ 15.) The lifespan of U.S. citizens follows a normal distribution with µ = 75 and a standard
deviation of 2 years. The middle 95% of all U.S. citizens live between (75 - 2*(2)2) and
(75+2*(2)2).
The Normal Distribution Model
In a normal distrubution, what percent of the values lie:
- Below the mean?
- Above the mean?
- Within one standard devaition of the mean?
- Within two standard deviations of the mean?
- Within three standrad deviations of the mean?
2000 freshmen at Iowa State University took a biology test. The scores were distributed normally with a mean of 70 and a standard deviation of 5. Draw a normal distribution and lable the mean and three standard devaitons from the mean.
Answer the follwing questions based on the data.
- What percentage of scores are between scores 65 and 75?
- What percentage of scores are between scores 60 and 85?
- What percentage of scores is less than a score of 55?
- What percentage of scores is greater than a score of 80?
- Approxiamtely how many biology students scored between 60 and 70?
- Apporximately how many biology students socre between 55 and 60?
500 juinors at Central High School took the ACT last year. The scores were distributed normally with a mean of 24 and a standard deviation of 4. Draw a normal distribution and lable the mean and three standard diveaions from the mean.
- What percentage of socres are between scores 61 amd 82?
- What percentage of scores are between socres 75 and 82?
- What percentage of scores are between socres 61 and 89?
- What percentage of socres is less than a score of 61?
- What percentage of scrores is greater than a score of 96?
- Approximately how many algerba students scored between 61and 89?
- Approximately how many algerba students scored between 68 and 82?
- Approximately how many algerba students scored between 61and 75?
- Approximately how many algerba students scored between 69and 96?
- Approximately how many algerba students scored higher than 89?