Question

in the given probability distribution, 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).
describe the shape of the distribution.
the distribution and is

Explanation:

Step1: Analyze the probabilities for each value of \(x\)

We have \(P(0) = 0.1687\), \(P(1)=0.3341\), \(P(2) = 0.2870\), \(P(3)=0.1478\), \(P(4)=0.0368\), \(P(5)=0.0256\).

Step2: Check for symmetry

A symmetric distribution has \(P(x - \mu)=P(\mu - x)\) around the mean \(\mu\). Here, \(P(0)
eq P(5)\), \(P(1)
eq P(4)\), \(P(2)
eq P(3)\) (where \(\mu=\sum_{x = 0}^{5}xP(x)=0\times0.1687 + 1\times0.3341+2\times0.2870 + 3\times0.1478+4\times0.0368+5\times0.0256=1.6995\approx1.7\)).

Step3: Check for skewness

The tail of the distribution is on the side where the probabilities are decreasing more slowly. Since \(P(0)>P(5)\), \(P(1)>P(4)\), \(P(2)>P(3)\), the tail is on the right - hand side.

Answer:

The distribution is skewed and is skewed right.