Final answer:
To calculate the average class size, multiply the number of classes by their respective capacities, sum these values, and divide by the total number of classes. To find other statistics like the PDF, mean, and standard deviation, one must consider the distribution of students across the different class sizes.
Step-by-step explanation:
The question pertains to finding the average class size and other statistical measures for a given distribution of class sizes at a university for its Summer 2013 term. To find the average class size (assuming each class is filled to capacity), we first need to multiply the number of classes by their respective capacities and then sum these amounts. Next, we divide by the total number of classes to get the mean:
- 1 class × 30 students = 30
- 8 classes × 60 students = 480
- 1 class × 70 students = 70
- 4 classes × 100 students = 400
The total number of students is 30 + 480 + 70 + 400 = 980. The total number of classes is 14. Hence, the average class size is 980 ÷ 14 = 70 students.
To calculate the probability density function (PDF) for X, the size of a randomly chosen student's class, and subsequent statistics such as the mean and the standard deviation, we should note the proportion of students in each class size and use these to find the expected value and variance.
To determine the mean number of students per statistics class across your state, a detailed sampling method would involve selecting a representative sample of statistics classes, possibly ensuring a mix of different class sizes, locations, and institution types. This could involve a stratified random sampling or a simple random sampling approach to ensure a diverse and representative sample is obtained.