The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determine.
1.37
1.32
1.47
1.1
1.80
The mean of a binomial random variable is given by μ = np.
Therefore, μ = 9 * 0.3 = 2.7.
So, the mean is 2.7.
The standard deviation of a binomial random variable is given by σ = √(np(1-p)).
Therefore, σ = √(9 * 0.3 * (1-0.3)) = √(1.89 * 0.7) = √1.323 = 1.15 (rounded to 2 decimal places).
So, the standard deviation is 1.15.
Using the Empirical Rule, approximately 68% of the data falls within 1 standard deviation of the mean.
So, the answer closest to 1 standard deviation away from the mean of 2.7 is 1.32.
Therefore, the answer is 1.32.