It looks like you've uploaded an image with a set of probability and statistics exercises. I'll go over each task briefly and provide help where needed:

1. Calculate Mean and Standard Deviation:

   • (a) Data: $1; 5; 3; 5; 2$ without GTR (technology).
   • (b) Data: $2.2; 3.7; 0.1; 9.4; 1.1; 0.1$ with GTR.

2. Mean and Standard Deviation for Frequency Distribution:

   • Two tables provided, one for GTR (technology use) and one without. These require using frequency-weighted mean and standard deviation formulas.

3. Spinning Wheel with Two Spins:

   • The random variable $X$ is the sum of the outcomes. You need to:
     • (a) Create a probability distribution for $X$, draw the graph.
     • (b) Calculate $P(X \geq 7)$.
     • (c) Calculate $P(2 \leq X \leq 4)$.

4. Expected Value and Standard Deviation for Task 3:

   • Compute these using the distribution from Task 3.

5. Simulate 100 Spins (from Task 3):

   • Use the expected value and standard deviation of empirical data to compare with Task 4.

6. Fairness of a Game:

   • (a) The table shows different values of $g$ (gain/loss). Check if the game is fair based on expected value.
   • (b) Adjust the win amount for $g = 5$ to make the game fair.

7. Binomial Probability:

   • (a) Describe a situation where you use the binomial formula $\binom{20}{4} \cdot 0.6^4 \cdot 0.4^{16}$.
   • (b/c) Calculate and interpret $\binom{20}{4}$.

8. Bernoulli Chain (Probability = $\frac{1}{3}$):

   • Various tasks based on hitting probability.

9. Red and Green Balls Problem:

   • Use combinatorics to calculate different outcomes with 8 balls, mixing red and green.

10. Number of Sixes in 45 Dice Rolls:

    • Compute expected value and standard deviation for the number of sixes.

Would you like detailed solutions for any of these tasks, or for a specific problem? Let me know which you'd prefer!

Here are some related questions:

1. How is the standard deviation formula applied to frequency distributions?
2. What methods can be used to calculate the probability distribution for Task 3?
3. How do you verify if a game is fair using expected value?
4. What is the binomial coefficient and how is it used in probability?
5. How do Bernoulli processes apply to real-world probability problems?

Tip: Remember, for calculating standard deviation, it's essential to keep track of whether you're using sample or population data, as the formulas slightly differ.