The prize for winning a contest can be chosen from category A or category B. Prizes from
category A have a mean of $1000 and a standard deviation of $50. Prizes from category B
have a mean of $1000 and a standard deviation of $300. Describe an advantage of each prize
category.
Category A Advantage:
The advantage of choosing a prize from category A is that the standard deviation is significantly smaller (only $50) compared to category B. This means that the prizes in category A are more consistent, with less variability. As a result, you can expect to receive a prize that is closer to the mean of $1000, ensuring a more predictable outcome. This may be favorable if you prefer a safer and more reliable prize.
Category B Advantage:
The advantage of choosing a prize from category B is that there is a higher potential for larger prizes. Despite having a larger standard deviation ($300), which indicates more variability in prize values, category B prizes may have a greater range of values than category A. This means that while there is a chance of receiving a prize lower than or equal to $1000, there is also a possibility of receiving a prize that exceeds $1000. If you are willing to take a bit more risk for a chance at a higher reward, category B may be more appealing to you.
The advantage of choosing a prize from category A with a mean of $1000 and a standard deviation of $50 is that the prize values are more tightly clustered around the mean. This means that there is less variability in the prize amounts, and you are more likely to win a prize closer to the mean value of $1000. This can give you a greater level of certainty in what you will receive.
On the other hand, the advantage of choosing a prize from category B with a mean of $1000 and a standard deviation of $300 is that the prize values are more widely spread out. While it is less likely to receive a prize exactly equal to the mean value of $1000, there is a higher potential to win a prize that is significantly higher than $1000. This category offers a greater opportunity for potentially larger rewards, although they come with a higher level of uncertainty.
In summary, the advantage of category A is the greater certainty of winning a prize closer to $1000, while the advantage of category B is the potential for larger rewards, albeit with a higher level of uncertainty. The choice ultimately depends on the individual's preference for a more predictable or potentially more lucrative outcome.
A ... the lowest prize is not far from the mean
B ... you COULD win almost double the mean