Final answer:
In a statistics class of 50 students, the probability of at least 40 doing their homework on time is calculated using the binomial probability distribution. Constructing a bar graph requires clear labeling and accurate representation of the data for students' birthdays by seasons. Improving resources and technology, such as using calculators and computers, can significantly increase efficiency in completing homework assignments.
Step-by-step explanation:
Probability Calculation in Statistics
For a statistics class of 50 students where approximately 70 percent do their homework on time, we can calculate the probability of at least 40 students doing their homework on time using the binomial probability formula. The formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'n' is the total number of students, 'k' is the number of students completing homework, and 'p' is the probability of a student completing homework on time. Since each student does homework independently, we apply this formula or utilize a binomial probability distribution table to find the desired probability.
When creating a bar graph to show the distribution of students' birthdays across seasons, it is best to clearly label both axes, ensure each bar corresponds to a season, and align the bars with the number of students or percentage as per the given data.
To determine the average number of pairs of jeans a student owns, surveying classmates and calculating the mean of the collected data will yield the desired average.
The concept that homework and test problems using estimations and approximations rather than exact numbers is important in understanding real-world applications of mathematics where precise figures are rarely provided, making estimation skills valuable.
Improving resources and technology, such as using a calculator and a computer, can increase the efficiency of completing homework, demonstrating a real-life application of the production possibilities concept in economics.