Question

current objective
create and interpret a binomial distribution with technology - calculator

first up, lets review the assignments learning objectives
get familiar with this topic by reviewing instruction and answering a couple of questions.

question
in a recent baseball season, ron was hit by pitches 19 times in 596 plate appearances during the regular season. assume that the probability that ron gets hit by a pitch is the same in the playoffs as it is during the regular season. in the first playoff series, ron has 22 plate appearances. what is the probability that ron will get hit by a pitch exactly once? use a ti-83, ti-83 plus, or ti-84 calculator to find the probability.

• round your answer to three decimal places.

provide your answer below:

Explanation:

Step1: Calculate success probability

$p = \frac{19}{596} \approx 0.0319$

Step2: Define binomial parameters

$n=22$, $k=1$, $p\approx0.0319$

Step3: Apply binomial probability formula

The binomial probability formula is:
$$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$
Substitute values:
$$\binom{22}{1} (0.0319)^1 (1-0.0319)^{22-1}$$
$$=22 \times 0.0319 \times (0.9681)^{21}$$

Step4: Compute the result

First calculate $(0.9681)^{21} \approx 0.513$, then:
$22 \times 0.0319 \times 0.513 \approx 0.361$

Answer:

0.361