Question

the following table represents the probability of the number of cars owned by a college student. give your answer to at least 3 decimal places.

a) is this a valid discrete probability distribution? select an answer

b) find the mean number of cars owned.

c) find the standard deviation of the number of cars owned.

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Explanation:

Step1: Check validity of discrete probability distribution

For a discrete probability distribution, \(\sum P(x)=1\) and \(0\leq P(x)\leq1\) for all \(x\).
\(\sum P(x)=0.47 + 0.33+0.13 + 0.07=1\) and each \(P(x)\) is between \(0\) and \(1\). So it is a valid discrete probability distribution.

Step2: Calculate the mean \(\mu\)

The formula for the mean of a discrete probability distribution is \(\mu=\sum xP(x)\)

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Step3: Calculate the variance \(\sigma^{2}\)

The formula for the variance is \(\sigma^{2}=\sum(x-\mu)^{2}P(x)\)

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\(\sigma^{2}=0.3008+0.0132 + 0.1872+0.3388=0.84\)

Step4: Calculate the standard deviation \(\sigma\)

The standard deviation \(\sigma=\sqrt{\sigma^{2}}\), so \(\sigma=\sqrt{0.84}\approx0.917\)

Answer:

a) Yes, it is a valid discrete probability distribution.
b) \(0.8\)
c) \(0.917\)