Questions: A random variable is binomially distributed with n=16 and π=.40. The expected value and standard deviation of the variables are Multiple Choice 2.00 and 1.24. 4.80 and 4.00 . 6.40 and 1.96. 2.00 and 1.20.

Solution Steps

The expected value (mean) of a binomially distributed random variable can be calculated using the formula:

\[ \mu = n \cdot p \]

Substituting the given values \( n = 16 \) and \( p = 0.40 \):

\[ \mu = 16 \cdot 0.40 = 6.4 \]

The variance of a binomially distributed random variable is given by the formula:

\[ \sigma^2 = n \cdot p \cdot q \]

where \( q = 1 - p \). Thus, \( q = 1 - 0.40 = 0.60 \). Now substituting the values:

\[ \sigma^2 = 16 \cdot 0.40 \cdot 0.60 = 3.84 \]

The standard deviation is the square root of the variance:

\[ \sigma = \sqrt{n \cdot p \cdot q} = \sqrt{3.84} \approx 1.96 \]

Final Answer