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Chapter 4, Problem 1CSE(choose chapter or problem)
Construct a probability distribution for
(a) the number of hits in games with three at-bats.
(b) the number of hits in games with four at-bats.
(c) the number of hits in games with five at-bats.
Questions & Answers
QUESTION:
Construct a probability distribution for
(a) the number of hits in games with three at-bats.
(b) the number of hits in games with four at-bats.
(c) the number of hits in games with five at-bats.
ANSWER:Step 1 of 3:
Our goal is:
a). We need to find the probability of the number of hits in games with 3 at-bats.
b). We need to find the probability of the number of hits in games with 4 at-bats.
c). We need to find the probability of the number of hits in games with 5 at-bats.
a). The probability is the frequency given in the histogram (at the top of the bar(s)), divided by the total frequency.
\(\begin{array}{l} P(x)=\frac{\text { The frequency given in the histogram }}{\text { The total frequency }} \\ P(x=0)=\frac{12}{12+12+6+0} \\ P(x=0)=\frac{12}{30} \\ P(x=0)=0.4 \end{array}\)
Then the probability that the number of hits in games with 3 at-bats table is given below,
\(\begin{array}{|c|c|} \hline \text { Number of hits } & P(x) \\ \hline 0 & \frac{12}{30}=0.4 \\ \hline 1 & \frac{12}{30}=0.4 \\ \hline 2 & \frac{6}{30}=0.2 \\ \hline 3 & \frac{0}{30}=0 \\ \hline \end{array}\)