Final answer:
The average time between fireworks in the show is 3 seconds. The probability of the time between fireworks being greater than four seconds is 0.25.
Step-by-step explanation:
In a fireworks show where the time between fireworks follows a uniform distribution of 1 to 5 seconds, we can find the average time between fireworks by taking the average of the minimum and maximum values. To calculate this, we add the minimum and maximum values and divide by 2:
average time = (1 + 5) / 2 = 3 seconds
To find the probability that the time between fireworks is greater than four seconds, we need to find the proportion of the range of time that is greater than four seconds. Since the range is 1 to 5 seconds, we subtract the proportion of the range that is less than or equal to four seconds:
probability = (5 - 4) / (5 - 1) = 0.25