Find the Specified Probability Distribution of the Binomial Random Variable

question 10

Multiple Choice

Find the specified probability distribution of the binomial random variable.
-In one city, the probability that a person will pass his or her driving test on the first attempt is 0.69. Four people are selected at random from among those taking their driving test for the first time. Determine the probability distribution of X, the number among the four who pass the test.

• A)
• \(\begin{array}{r|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.0092 \\
• 1 & 0.0822 \\
• 2 & 0.2745 \\
• 3 & 0.4074 \\
• 4 & 0.2267
• \end{array}\)
• B)
• \(\begin{array}{c|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.0092 \\
• 1 & 0.0822 \\
• 2 & 0.1830 \\
• 3 & 0.4074 \\
• 4 & 0.2267
• \end{array}\)
• C)
• \(\begin{array}{r|r}
• \mathrm{x} & \mathrm{P}(X=\mathrm{X}) \\
• \hline 1 & 0.69 \\
• 2 & 0.4761 \\
• 3 & 0.3285 \\
• 4 & 0.2267
• \end{array}\)
• D)
• \(\begin{array}{c|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.0092 \\
• 1 & 0.0822 \\
• 2 & 0.2745 \\
• 3 & 0.4254 \\
• 4 & 0.2087
• \end{array}\)

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Definitions:

Long Run Aggregate-Supply

In economics, it represents the total quantity of goods and services that producers in an economy are willing and able to supply at a full employment level, regardless of the price level, over a long period.

Long-Run Equilibrium

A state in which all factors of production are optimally allocated, and firms in a competitive market have no incentive to change their output level or enter/exit the industry.

Expected Price Level

The anticipated average level of prices in the economy for goods and services, often considered in the context of inflation expectations.

Aggregate Supply

The total supply of goods and services produced within an economy at a given overall price level in a given period.