Montgomery College Binomial Distribution & Histogram Questions

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Experience 5 – The Binomial Distribution

Questions:

1. How do you know when to use the binomial distribution to model a situation? What are the requirements for a binomial experiment? [4 bullets]
2. When dealing with the binomial distribution, why are the possible values for the random variable always 0,1,2,3,…,n where n is the number of trials or sample size? Why can’t we use negative values, or fractions, or numbers greater than n? [3 sentences]
3. Under what conditions is a binomial distribution symmetric? Skewed left? Skewed right? Why? [3 sentences]
4. How is the area in the bars of a binomial histogram related to the probability of choosing those X values? (Hint: figure it out for a single bar) [3 sentences]

Experience 6 – Continuous Probability Distributions

Critical Thinking Questions

1. What does a z-score tell you about a number in a data set? [1 sentence]
2. What two quantities do we need to fully describe a normal distribution? [1 sentence]
3. How is probability determined from a continuous distribution? Why is this easy for the uniform distribution and not so easy for the normal distribution? [2 sentences]
4. What does the symmetric bell shape of the normal curve imply about the distribution of individuals in a normal population? [2 sentences]
5. How can the empirical rule be restated in terms of z-scores and percentiles? Restate it for four of the seven z-scores. Hint: Use the definitions of z-score and percentile and avoid use of the phrase “standard deviation” or the numbers 68, 95, and 99.7. [4 statements]

Experience 7 – Normal Distributions

Critical Thinking Questions

1. Why is the probability that a continuous random variable is equal to a single number zero? (i.e. Why is P(X=a)=0 for any number a) [1 sentence]
2. In what ways can a quick drawing of the normal curve (not a detailed empirical rule drawing but a simple one like that shown in the instructor’s video) be used to estimate or verify your answer to a problem like practice exercises 2-4? [2 sentences]
3. The empirical rule says that 95% of the population is within 2 standard deviations of the mean, but when I find the z-scores that mark off the middle 95% of the standard normal distribution I calculate -1.96 and 1.96. Is this a contradiction? Why or why not? In other words why are the normal distribution calculators not agreeing with the empirical rule? [2 sentences]
4. Suppose you randomly select an individual from a population that is normally distributed and they are above average. When you find out the probability of randomly selecting that individual is very very small, what are some possible explanations? In other words what does this very very small probability suggest? [3 sentences]