statistics assignment 4

Probability And Statistics | Week 4

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These are Probability And Statistics Week 4 Assignment 4 Answers

Q1. The number of phone calls over a certain time period follows a Poisson distribution. What is the average number of calls necessary for the probability of one or more calls is at least 0.98? (A) 5 (B) 4 (C) 3 (D) 1

Answer: (B) 4

Q2. The total duration of all games by one team in one season of a major baseball league is seen to range uniformly between 427 hours to 504 hours. What is the probability that a team will play between 479 to 498 hours of games in a season? (A) 0.247 (B) 0.377 (C) 0.521 (D) 0.232

Answer: (A) 0.247

Q3. Assume that the time taken to finish a standard sized piece of cake by a nine-year-old child is uniforml distributed between 0.5 and 3 minutes. Given that a child has been eating the cake for more than 1.5 minutes, determine the probability that he/she will finish it in more than two minutes? (A) 4/5 (B) 1/2 (C) 2/3 (D) 3/4

Answer: (C) 2/3

Q4. Maximum time to complete a project is 2.5 days. Suppose the completion time as a proportion of this maximum time is a beta random variable with a =2 and ß = 3. What is the probability that the project requires more than two days to complete? (A) 0.03 (B) 0.07 (C) 0.09 (D) 0.009

Answer: (A) 0.03

Q5. With an average of 10,000 miles, the number of miles a particular car may travel before experiencing battery failure is exponentially distributed. The car’s owner needs to travel 4000 miles. What is the probability that the journey can be finished without a car battery replacement? (A) e -0.6 (B) e -0.4 (C) 0.4e -0.4 (D) 0.6e -0.6

Answer: (B) e -0.4

Q6. The life of an MRI machine is modelled by a Weibull distribution with cumulative density function given by F(x) = 1 – e-(-², x ≥ 0, where parameters ß = 3 and 8 = 700 hours. What is the probability that the MRI fails before 350 hours? (A) 0.258 (B) 0.169 (C) 0.277 (D) 0.117

Answer: (D) 0.117

Q7. The time needed to solve a problem has an exponential distribution with Λ = 1/3. Two students, start tackling the problem simultaneously. (Assume the students are working independently on their own.) At the end of the two minutes, what is the probability that at least one student has figured out the problem? (A) 0.234 (B) 0.642 (C) 0.264 (D) 0.736

Answer: (D) 0.736

Q8. Suppose X is a random variable with distribution function to be a Beta distribution (Beta(a, ß)). The mean and standard deviation of X are 0.09 and 0.03 respectively. Find the parameters (a, ß). (A) (a, ß) = (8.1,81.9) (B) (a, ß) = (3.8,91.2) (C) (a, ß) = (7.1,82.9) (D) (a, ß) = (17.1,72.9)

Answer: (A) (a, ß) = (8.1,81.9)

Q9. A Poisson process governs website hits, with a mean of 20 every hour. What is the probability that there won’t be any hits on the website in a 12-minute period? (A) 0.670 (B) 0.961 (C) 0.220 (D) 0.952

Answer: (A) 0.670

Q10. Calls to a customer care number follow a Poisson distribution with a mean of 25 calls per minute. What is the mean time until the 100th call? (A) 1 (B) 8 (C) 4 (D) 5

Answer: (C) 4

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Statistics Assignment Examples

February 2, 2024

Introduction: Embarking on the intricate journey of statistics assignments can be both challenging and enlightening. To navigate this terrain successfully, gaining a deep understanding of statistical concepts is crucial. In this comprehensive exploration, we’ll delve into the world of statistics assignment examples, unraveling the complexities through real-world scenarios. Whether you’re a student seeking clarity for your assignments or an enthusiast eager to grasp the practical applications of statistics, join us on this illuminating journey with Statistics Homework Tutors. Together, we’ll dissect key statistical concepts using practical examples, providing you with the tools to master this field and transform challenges into triumphs.

The Essence of Descriptive Statistics: Shedding Light on Performance

Example 1: exam scores.

Imagine you’re a student in a class of 30, eagerly awaiting your math exam scores. Descriptive statistics come to the rescue, turning those numbers into meaningful insights:

Average (Mean): Calculating the sum of all scores and dividing by the number of students provides a snapshot of the overall performance.
Middle Value (Median): Arranging scores in ascending order and identifying the middle score offers a representation of central tendency.
Most Frequent Score (Mode): Spotting the score that appears most frequently gives a sense of the prevailing performance level.

This statistical approach transforms a seemingly random set of scores into a clear understanding of the class’s academic standing.

Harnessing the Power of Inferential Statistics: Predicting Outcomes

Example 2: opinion polls.

In the world of politics, predicting election outcomes is a task tailor-made for inferential statistics. Imagine conducting an opinion poll with 1,000 participants to gauge voter preferences:

Hypothesis Testing: Evaluating whether a particular candidate’s popularity significantly differs from others provides insights into voter sentiment.
Confidence Intervals: Estimating the range within which the true proportion of voters supporting a candidate lies adds a layer of certainty to predictions.

Inferential statistics empowers us to draw meaningful conclusions about a larger population based on a representative sample.

Business Optimization through Regression Analysis

Example 3: sales and advertising.

Enter the dynamic world of business, where regression analysis plays a pivotal role in optimizing advertising strategies. Consider a scenario where a company invests in advertising campaigns over several months:

Modeling Relationships: Establishing a mathematical relationship between advertising expenses and sales unveils the dynamics at play.
Predicting Outcomes: Anticipating the expected increase in sales for a given increase in advertising spending guides decision-making.

Regression analysis transforms data into actionable insights, aiding businesses in making informed choices to maximize their impact.

Quantifying Uncertainty with Probability Distributions

Example 4: coin toss.

Dive into the world of probability distributions with a simple coin toss. The unpredictability of this event is quantified through:

Likelihood of Outcomes: A fair coin offers a 50% chance of landing on heads or tails, illustrating the fundamental concept of probability.
Expected Value: The average outcome over many tosses converges to 0.5, showcasing the stability of probability predictions.

Understanding probability distributions is fundamental to making sense of uncertainties and predicting outcomes in various scenarios.

Real-World Impact: Statistics in Healthcare

Example 5: medical diagnosis.

In the critical realm of healthcare, statistics takes center stage in medical diagnosis. Consider a diagnostic test for a rare disease:

Sensitivity and Specificity: Evaluating the accuracy of the test in identifying true positives and true negatives helps in assessing its reliability.
False Positive Rate: Examining the likelihood of a healthy person receiving an incorrect diagnosis adds a layer of caution.

Statistics in healthcare guides medical professionals in interpreting test results, making accurate diagnoses, and ultimately improving patient outcomes.

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