If a city will be randomly selected from those that have at least 10 days with precipitation, what is the probability that the city selected will have a daily low temperature greater than 30 degrees Fahrenheit?
The probability that the city selected will have a daily low temperature greater than 30 degrees Fahrenheit is {2/5}.
This probability indicates that out of the cities that meet the precipitation criteria, 40% have daily low temperatures exceeding 30 degrees Fahrenheit. This ratio reflects the specific subset of cities within the total that aligns with the stated temperature condition.
This choice suggests that only one out of every six cities has a daily low temperature greater than 30 degrees Fahrenheit. However, this underestimates the actual number of qualifying cities, as it does not align with the data indicating a higher proportion of cities meeting the temperature threshold.
Selecting {1/3} implies that one-third of the cities with at least 10 days of precipitation have daily low temperatures above 30 degrees Fahrenheit. This is an over-simplification, as the actual data shows a larger fraction of cities surpassing this threshold, thus making this answer inaccurate.
Choosing {1/2} indicates an equal split of cities below and above the 30 degrees Fahrenheit mark. This choice misrepresents the actual distribution of cities, as the probability of having daily low temperatures greater than 30 degrees is less than half among those qualifying cities.
This option correctly represents the proportion of cities with daily low temperatures exceeding 30 degrees Fahrenheit, showing that two out of five cities fit the criteria. This accurately reflects the relationship between the given conditions and the data analyzed.
This selection suggests that two-thirds of the cities have daily low temperatures above 30 degrees Fahrenheit. This is an overestimation, as it does not correspond to the actual findings where a smaller percentage of cities meet this criterion.
The correct probability of selecting a city with a daily low temperature greater than 30 degrees Fahrenheit is {2/5}, which accurately reflects the statistical data derived from the cities with at least 10 days of precipitation. The other options fail to represent the actual ratios, either underestimating or overestimating the number of qualifying cities, thus reinforcing the validity of the correct choice.
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