Computing Binomial Probabilities A Stats 10 test has 4 multiple choice

# Computing binomial probabilities a stats 10 test has

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Computing Binomial ProbabilitiesA Stats 10 test has 4 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 4 questions, what is the probability that you get exactly 1 question correct? a) 0.04668 b) 0.42188 c) 0.10547 d) 0.25
Binomial Distribution Function The formula that finds the probabilities for the binomial distribution for probability of success p, fixed number of trials n, and k successes is as follows:
Binomial Coefficient The n over the k inside the parentheses can be read as “n choose k” Instead of writing all different combinations of outcomes and counting them all one-by-one this provides us the number of all those combinations.
Factorials ! - indicates a factorial n! = n x (n-1) x (n-2) x (n-3) x .... x 1 5! = 5 x 4 x 3 x 2 x 1 = 120 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Binomial Coefficient Examples
Binomial Coefficient Hints
Computing Binomial Probabilities A Stats 10 test has 4 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 4 questions, what is the probability that you get exactly 2 questions correct? Using the binomial probability function:
Computing Binomial ProbabilitiesA Stats 10 test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get exactly 2 questions correct?
Computing Binomial Probabilities A Stats 10 test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get 4 or more questions correct?
Computing Binomial ProbabilitiesA Stats 10 test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get at least 1 question correct?
Expected Value and Standard Deviation The mean and standard deviation of the binomial can be easily calculated Their interpretation is the same as with all distributions. Mean is the center and standard deviation tells us how far values typically are from the mean. Expected value or Mean = np Standard deviation =
Expected Value Example A Stats 10 test has 4 multiple choice questions with one correct answer each. If we just randomly guess on each of the 4 questions, what is the expected number of questions we get correct? Expected value = np = 4 x 0.25 = 1 Standard deviation = = 0.866 We are expected to only get 1 out of 4 questions correct if we just randomly guess.
Continuous Probability Distribution Function Often represented as a curve The area under the curve between two values of x represents the probability of x being between the two values The total area under the curve must equal 1 The curve cannot lie below the x-axis
The Normal Model is a good fit if: The distribution is unimodal The distribution is approximately symmetric The distribution is approximately bell shaped A Normal distribution is defined by the mean and standard deviation . Shorthand for a normal distribution is N( , ) The Normal distribution is also called the Gaussian distribution or the Bell Curve The Normal Model
Standardizing with z-scores Reminder: z-scores are standardized scores