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Accel Math III Unit #1: Data Analysis Lesson #7: Calculating Mean, Variance, and Standard Deviation for a Binomial Distribution EQ: How do you calculate mean, variance, and standard deviation of a binomial distribution and how are these used to interpret the data? Recall: Create a probability distribution where the random variable of interest is number of heads occurring when tossing 4 coins. [HINT: You can, but you don’t have to create a sample space to complete this task.] X P(X) Find the expected value for this task. E(X) = __________________________ Now calculate (n)(p) Formula: ______________ Mean of a Binomial Distribution µ = __________________ Find the variance for this task. σ2 = ____________________________ Now calculate (n)(p)(q) ______________ Formula: σ2 Variance of a Binomial Distribution = ____________________________ Find the standard deviation for this task. σ = _____________________ Now calculate (n)( p)(q) _____________ Formula: Standard Deviation of a Binomial Distribution σ = _____________________ Ex 1. A die is rolled 480 times. Find the mean, variance, and standard deviation of the number of 2’s that will be rolled. µ = __________________ σ2 = ________________ σ = _____________________ Ex 2. The Statistical Bulletin published by Metropolitan Life Insurance Co. reported that 2% of all American births result in twins. If a random sample of 8000 births is taken, find the mean, variance, and standard deviation of the number of births that would result in twins. µ = __________________ σ2 = ________________ σ = _____________________ Ex 3. Assignment: Practice Worksheet: Calculating Mean, Variance, and Standard Deviation of Binomial Distributions Test #1 Unit 1