Number Of Hits Frequency Number Of Hits With 4 At Bats

Number Of Hits Frequencynumber Of Hits With 4 At Bats012

Number Of Hits Frequencynumber Of Hits With 4 At Bats012

Number of Hits Frequency Number of Hits with 4 At-Bats Number of Hits Frequency No. of Successes Frequency No. of Successes in 5 Shots Freq., f No. of Successes Frequency Option #1: Batting The batting average of a baseball player is the number of “hits†divided by the number of “at-bats.†Recently, a certain major league player’s at-bats and corresponding hits were recorded for 200 consecutive games. The consecutive games span more than one season. Since each game is different, the number of at-bats and hits both vary. For this particular player, there were from zero to five at-bats. Thus, one can sort the 200 games into six categories: 0 at-bats 1 at-bat 2 at-bats 3 at-bats 4 at-bats 5 at-bats Consider the games where the player had exactly four at-bats.

A similar analysis can be done for each of the other at-bats category. Download the file titled Bats. It contains a scatter plot of the four at-bats number of hits versus frequency. To compare the results to the Binomial Distribution, complete the following: 1. Explain why the four at-bats is a binomial experiment. 2. Using the Bats scatter plot, construct a frequency distribution for the number of hits. 3. Compute the mean number of hits. The formula for the mean is .

Here, xi represent no. of hits (0, 1, 2, 3, 4) and fi is the corresponding frequency. Explain what the numerical result means. 4. From the frequency distribution, construct the corresponding probability distribution. Explain why it is a probability distribution.

Then, use Excel to make a scatter plot of the probability distribution: Select the two columns of the probability distribution. Click on INSERT, and then go to the Charts area and select Scatter. Then choose the first Scatter chart (the one without lines connecting). 5. Using the frequency distribution, what is the player’s batting average for four at-bats?

In part 3, note that the numerator in the formula for the mean is the total number of hits. The total number of at-bats is the denominator of the formula for the mean multiplied by 4. 6. The Binomial Distribution is uniquely determined by n, the number of trials, and p, the probability of “success†on each trial. Using Excel, construct the Binomial Probability Distribution for four trials, n, and probability of success, p, as the batting average in part 5.

Here is an explanation of the BINOM.DIST function (Links to an external site.)Links to an external site. in Excel. For example, In Excel =BINOM.DIST(7,15,0.7, FALSE) represents the probability of 7 successes out of 15 (n) trials. The 0.7 is the probability of success, p. 7. Using the formula for the mean of the binomial distribution, what is the mean number of successes in part 6 up above?

8. In Excel, make a scatter plot for the binomial distribution. The instructions for making one are in part 4 up above. 9. Use the results up above to compare the probability distribution of four at bats and the Binomial Distribution.

Compare the means in parts 4 and 6, too. If the probability distribution of 4 at bats and the Binomial Distribution differ, explain why that is so. Write a report that adheres to the Written Assignment Requirements under the heading “Expectations for CSU-Global Written Assignments†found in the CSU-Global Guide to Writing and APA Requirements (Links to an external site.)Links to an external site. . As with all written assignments at CSU-Global, you should have in-text citations and a reference page. An example paper is provided in the MTH410 Guide to Writing with Statistics.

Submit your Excel file in addition to your report. Requirements: 1. Paper must be written in third person. 2. Your paper should be four to five pages in length (counting the title page and references page) and cite and integrate at least one credible outside source.

3. Include a title page, introduction, body, conclusion, and a reference page. 4. The introduction should describe or summarize the topic or problem.

It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic. 5. The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.

6. The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs. 7. Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.

Paper For Above instruction

The evaluation of a baseball player's batting performance over a series of games provides an insightful application of probability distribution concepts, particularly the binomial distribution. This analysis hinges on understanding why certain game data can be modeled as binomial experiments, constructing frequency and probability distributions from real data, and comparing these empirical results to theoretical binomial models using Excel tools. Such an approach not only deepens statistical comprehension but also enhances understanding of real-world sports analytics.

Firstly, the categorization of games based on the number of at-bats for a player (ranging from zero to five) reflects discrete, independent trials with fixed probability of success—each at-bat—making it a binomial experiment. The key characteristics—fixed number of trials, binary outcomes as hits or misses, and independence of each at-bat—are foundational for binomial modeling. Specifically, when examining games where the player had exactly four at-bats, the scenario naturally aligns with the binomial experiment framework, since each at-bat can be viewed as a Bernoulli trial with a success probability, representing whether the player gets a hit or not.

Constructing an empirical frequency distribution from the scatter plot provided in the dataset (downloaded as 'Bats') allows observation of the distribution's shape regarding the number of hits in four at-bats. Data extraction involves tallying the frequency of each possible number of hits (from zero to four). Calculating the mean number of hits—using the formula: mean = Σ (xi * fi) / total games—provides an average performance metric over the 200 recorded games. For instance, a calculated mean of 1.4 hits suggests that the player, on average, obtains about 1.4 hits in four at-bats per game, indicating a batting success rate that influences subsequent probability modeling.

Translating the frequency distribution into a probability distribution involves dividing each frequency by the total number of games (200). This converts raw counts into probabilities that sum to one, satisfying the fundamental property of probability distributions. Constructing a scatter plot of this probability distribution via Excel visualizes the empirical likelihood of each number of hits, enabling comparative analysis against the theoretical binomial distribution.

The empirical batting average in this context is the ratio of total hits to total at-bats across all relevant games. Specifically, the total hits divided by the total at-bats yields the player’s batting average, which in this analysis corresponds to the probability of success (p) in the binomial model.

The binomial probability distribution is explicitly constructed by selecting the number of trials (n = 4) and the probability of success (p) derived from the empirical batting average. Using Excel’s BINOM.DIST function, the probability of obtaining exactly k successes (hits) in four trials can be calculated for each k from 0 to 4. These probabilities form the theoretical binomial model, which can then be plotted as a scatter diagram following the same method as the empirical probabilities.

Calculating the mean number of successes for the binomial distribution uses the formula: mean = n * p. Comparing this with the empirical mean from earlier provides insights into the consistency of the model with observed data. Discrepancies between empirical and theoretical distributions can occur due to factors such as variability in performance, the assumption of independence, or sample size limitations.

Finally, comparing the empirical probability distribution with the binomial distribution offers a broader understanding of the player's performance relative to a statistical model. Close alignment suggests that the binomial model is appropriate, while significant differences could indicate underlying factors not captured by simple binomial assumptions. The analysis emphasizes the importance of understanding theoretical models, data-driven insights, and the role of computational tools like Excel in sports statistics and probabilistic analysis.

In conclusion, modeling the batting performance of a baseball player using binomial distributions underscores the practicality of probability theory in sports analytics. This approach facilitates a nuanced understanding of player success rates, informs strategic decisions, and exemplifies how statistical tools can interpret real-world performance data. As sports analytics continues to evolve, integrating empirical data with mathematical models allows for more precise and actionable insights, benefiting coaches, players, and fans alike.

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