Final answer:
To solve the problem, set up a system of inequalities using the given information. Graph the inequalities on a coordinate plane and shade the region that satisfies all the inequalities. Determine the probability based on the shaded region.
Step-by-step explanation:
To solve this problem, we can set up a system of inequalities based on the given information.
- Let x be the number of dimes.
- Let y be the number of nickels.
- The minimum number of coins is 20, so we have the inequality x + y ≥ 20.
- The maximum value of the combined coins is $1.60, so we have the inequality 0.1x + 0.05y ≤ 1.60.
- We also know that at least 4 of the coins are dimes, so we have the inequality x ≥ 4.
To solve this system of inequalities graphically, we can plot the points that satisfy each inequality on a coordinate plane and shade the region that satisfies all the inequalities. The intersection of the shaded region represents one possible solution to the problem.
The probability that an individual had between $0.80 and $1.00 can be found by determining the area of the shaded region between the corresponding values on the graph.
The probability that the average amount of change of 25 students was between $0.80 and $1.00 can be found by dividing the total area of the shaded region by the total area of the graph.
The difference between parts (e) and (f) is due to the fact that in part (e) we are considering the probability for an individual, whereas in part (f) we are considering the probability for the average amount of change for a group of individuals.