Question

the random variable x is the crew size of a randomly selected shuttle mission. its probability distribution is shown below. complete parts a through c.

a. find and interpret the mean of the random variable.
(mu=square) (round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for the mean of a discrete random variable

The formula for the mean \(\mu\) of a discrete random variable \(X\) is \(\mu=\sum_{x}x\cdot P(X = x)\).

Step2: Calculate each term \(x\cdot P(X = x)\)

• For \(x = 2\): \(2\times0.065=0.13\)
• For \(x = 3\): \(3\times0.009 = 0.027\)
• For \(x = 4\): \(4\times0.074=0.296\)
• For \(x = 5\): \(5\times0.367 = 1.835\)
• For \(x = 6\): \(6\times0.094=0.564\)
• For \(x = 7\): \(7\times0.356=2.492\)
• For \(x = 8\): \(8\times0.035 = 0.28\)

Step3: Sum up all the terms

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Answer:

\(\mu = 5.624\). The mean of the random variable \(X\) (crew - size) is \(5.624\). This means that, on average, the crew size of a randomly selected shuttle mission is approximately \(5.624\).