Final answer:
To find the probability that the average profit from a set of 10 tickets is between $-0.35 and $0.84, we need to calculate the probability distribution of the average profit using the Central Limit Theorem and the Z-score. With the given mean profit and assumptions, we can find the desired probability using a Z-table or calculator.
Step-by-step explanation:
To find the probability that the average profit from a set of 10 tickets is between $-0.35 and $0.84, we need to calculate the probability distribution of the average profit. The mean profit of a ticket can be calculated using the given expected values: 0(.969) + 5(.025) + 25(.005) + 100(.001) = $0.35.
Since we have the mean and we assume a normal distribution, we can use the Central Limit Theorem to approximate the probability distribution of the average profit. From there, we can find the probability that the average profit falls between $-0.35 and $0.84 using the Z-score.
The Z-score can be calculated as (X - mean) / (standard deviation), where X is the desired average profit, mean is the mean profit, and standard deviation is the standard deviation of the sample. Once we have the Z-score, we can find the corresponding probability using a Z-table or a calculator.