Business Statistics – There Are 8 Questions In Total, Each W

Business Statistics - There are 8 questions in total, each worth 12.5 points

Develop detailed solutions to the following eight business statistics questions, ensuring original work that has not been previously sold. The questions cover data analysis, probability, normal distribution, and statistical inference, requiring clear explanations, calculations, and interpretations of results.

Paper For Above instruction

Question 1

The dataset consists of temperature data and weather conditions for a selected Sunday across various world cities. It includes high and low temperatures (quantitative variables) and weather conditions indicated by categories: clear (c), cloudy (cl), showers (sh), and partly cloudy (pc).

1. The number of data elements corresponds to the total number of city observations captured for this Sunday. For example, if data were recorded from 10 cities, then there are 10 elements.

2. The variables include high temperature, low temperature, and weather condition, totaling three variables. Among these, temperature values are quantitative, and weather condition is categorical.

3. Observations refer to the individual data points collected per city. If data for 10 cities were recorded, then there are 10 observations.

4. Variables are: High Temperature (quantitative), Low Temperature (quantitative), Weather Condition (categorical).

Question 2

A student has completed 20 courses in the School of Arts and Sciences, with recorded grades. To analyze her performance:

1. Construct a frequency distribution by categorizing grades (e.g., A, B, C, D, F) and counting the number of courses for each grade. A bar chart visually displays these frequencies, illustrating the distribution of her grades.

2. Calculate the relative frequency for each grade class by dividing individual frequency counts by total courses (20). Then, create a pie chart to represent the proportion of each grade relative to her entire coursework.

Question 3

The data on hours worked per week for ten students is presented as a numeric list. To analyze:

1. The median is the middle value when the hours are ordered from lowest to highest. It indicates the typical central value of weekly hours worked.

2. To compute the 70th percentile, arrange data in ascending order and identify the value below which 70% of the observations fall. This percentile reflects the workload for more than two-thirds of students.

3. The mode is the most frequently occurring number of hours. It represents the most common weekly work hours among the students.

Question 4

Given probabilities for events A, B, C, and D:

1. Compute P(D) based on provided data or assumptions.

2. Calculate the joint probability P(A ∩ B) assuming independence or dependence information.

3. Find the conditional probability P(A | C) = P(A ∩ C) / P(C).

4. Determine the probability of the complement of C: P(C') = 1 - P(C).

5. A and B are mutually exclusive if P(A ∩ B) = 0; determine and explain.

6. A and B are independent if P(A ∩ B) = P(A) * P(B); analyze and justify.

7. Similarly, evaluate whether A and C are mutually exclusive and independent based on given data.

Question 5

Considering a machine producing non-defective items with an 80% success rate:

1. The probability that among three items, exactly one is defective can be modeled via the binomial distribution: P(X=1) = C(3,1) (0.8)^2 (0.2)^1.

2. Using the binomial probability function, confirm the likelihood of exactly one defective item and interpret the result.

Question 6

Starting salaries of graduates are normally distributed with mean $20,000 and standard deviation $8,000:

1. Calculate the probability a graduate earns at least $30,400 using z-scores and standard normal tables.

2. Determine the percentage earning less than $15,600 which qualifies them for a tax break, via z-scores.

3. Find the minimum and maximum salaries within the middle 95.4% of the data by using the 2.5th and 97.5th percentiles of the normal distribution.

Question 7

Data from 6 database programmers in Houston includes weekly incomes and sex. Estimations include:

1. The point estimate for the average weekly income is the sample mean.

2. The standard deviation of the sample indicates dispersion; use sample data to estimate the population deviation.

3. The proportion of female programmers is obtained by dividing the number of females by total sample size.

Question 8

Averages and variability of students' lunch expenditures are analyzed:

1. The mean expected expenditure is $5, with a standard deviation of $3, and the shape of the distribution approximates a normal curve due to the Central Limit Theorem, given the sample size.

2. Probability the sample mean exceeds $4 is calculated using the sampling distribution's properties.

3. Similarly, determine the probability that the sample mean is at least $5.90, applying z-scores and standard normal probabilities.

References

  • Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences (9th ed.). Cengage Learning.
  • Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers (6th ed.). Wiley.
  • Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & Statistics for Engineers & Scientists (9th ed.). Pearson.
  • Rice, J. A. (2007). Mathematical Statistics and Data Analysis (3rd ed.). Cengage Learning.
  • Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis (6th ed.). Cengage Learning.
  • Freund, J. E., & Williams, R. E. (2010). Modern Elementary Statistics (12th ed.). Pearson.
  • Nelson, J. (2014). Business Statistics: A First Course. Cengage Learning.
  • Gupta, S. C., & Kapoor, V. K. (2014). Fundamentals of Mathematical Statistics. S. Chand Publishing.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics (8th ed.). Pearson.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics (8th ed.). W. H. Freeman.

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