Can you set questions on statistics for a graduate focusing on confidence limit, probability, quadratic equations, exponents, and logarithm?

Steps to Solve

1. Define Topics for Graduate Level Questions
   Since the focus is on statistical questions related to confidence limits, probability, quadratic equations, exponents, and logarithms, let's start by briefly defining the key concepts:

   • Confidence Limits: These define a range of values that are likely to contain a population parameter.
   • Probability: This measures the likelihood of an event occurring.
   • Quadratic Equations: Equations that can be expressed in the form $ax^2 + bx + c = 0$.
   • Exponents: These indicate how many times a number (base) is multiplied by itself.
   • Logarithms: These are the inverse operations of exponentiation.

2. Create Statistical Questions
   Next, we will create specific statistical questions for each topic.

   • Confidence Limits:
     What is the 95% confidence interval for the mean weight of a sample of 50 individuals, where the sample mean is 75 kg and the standard deviation is 10 kg?

   • Probability:
     In a survey of 100 graduate students, if 60 students prefer online learning, what is the probability that a randomly selected student prefers online learning?

   • Quadratic Equations:
     A researcher finds that the relationship between supply (S) and price (P) can be modeled by the equation $S = -2P^2 + 120P - 240$. What is the price for which supply will be maximized?

   • Exponents:
     If the population of a city doubles every 10 years, and the current population is 50,000, what will be the population in 30 years?

   • Logarithms:
     What is the time required for an investment to triple if it is compounded annually at a rate of 5%, using the formula $A = Pe^{rt}$?

3. Ensure Clarity and Depth
   Confirm that each question promotes critical thinking and application of statistical methods suitable for graduate-level analysis.