Find the Specified Probability Distribution of the Binomial Random Variable

question 31

Multiple Choice

Find the specified probability distribution of the binomial random variable.
-A multiple choice test consists of four questions. Each question has five possible answers of which only one is correct. A student guesses on every question. Find the probability distribution of X, the
Number of questions she answers correctly.

• A)
• \(\begin{array}{c|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.4096 \\
• 1 & 0.4096 \\
• 2 & 0.1536 \\
• 3 & 0.0256 \\
• 4 & 0.0016
• \end{array}\)
• B)
• \(\begin{array}{c|r}
• x & P(X=x) \\
• \hline 1 & 0.4096 \\
• 2 & 0.1536 \\
• 3 & 0.0256 \\
• 4 & 0.0016
• \end{array}\)
• C)
• \(\begin{array}{l|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.4096 \\
• 1 & 0.4096 \\
• 2 & 0.1024 \\
• 3 & 0.0768 \\
• 4 & 0.0016
• \end{array}\)
• D)
• \(\begin{array}{c|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0 \\
• 1 & 0.2 \\
• 2 & 0.04 \\
• 3 & 0.008 \\
• 4 & 0.0016
• \end{array}\)

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Definitions:

Logarithm

A logarithm is the power to which a number, called the base, must be raised to produce a given number.

Fraction

A numerical quantity that is not whole, representing a part of a whole.

Inverse Function

A function that reverses the effects of another function, such that the composition of the two functions yields the identity function.

Graph

A visual representation of data or mathematical functions on a coordinate plane.