Question

in the probability distribution to the right, the random variable x represents the number of hits a baseball player obtained in a game over the course of a season. complete parts (a) through (f) below. describe the shape of the distribution. the distribution has one mode and is skewed right. (c) compute and interpret the mean of the random variable x. \\( \mu_{x}=\square \\) hits (type an integer or a decimal. do not round)

Explanation:

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

The formula for the mean \(\mu_X=\sum_{x}x\cdot P(x)\)

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

• When \(x = 0\): \(0\times0.1674=0\)
• When \(x = 1\): \(1\times0.3251 = 0.3251\)
• When \(x = 2\): \(2\times0.2877=0.5754\)
• When \(x = 3\): \(3\times0.1484 = 0.4452\)
• When \(x = 4\): \(4\times0.0378=0.1512\)
• When \(x = 5\): \(5\times0.0236 = 0.118\)

Step3: Sum up the terms

\(\mu_X=0 + 0.3251+0.5754+0.4452+0.1512+0.118\)
\(\mu_X=1.6149\)

Answer:

\(1.6149\)