The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determine.

Question

1.37


1.32


1.47


1.1


1.80

Answer 1

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.