Here's the five- number summary for the distribution of cigarette taxes (in cents) among the 50 states and Washington, D.C. in the United States.
Min. = 2.5, Q1= 36, Median = 60, Q3= 100, Max. = 205
About what proportion of the states have cigarette taxes (i) greater than 36 cents and (ii) greater than $1?
To find the proportion of states with cigarette taxes greater than a certain value, you need to use the information provided in the five-number summary.
(i) To find the proportion of states with cigarette taxes greater than 36 cents, you can use the third quartile (Q3) value. Q3 represents the value below which 75% of the data lies. In this case, Q3 is 100 cents.
So, the proportion of states with cigarette taxes greater than 36 cents is the same as the proportion of states with cigarette taxes greater than Q3, which is (Max - Q3) / 100. In this case, it would be (205 - 100) / 100 = 105 / 100 = 1.05.
However, proportions should be between 0 and 1, so we can treat any value above 1 as 1. Therefore, the proportion of states with cigarette taxes greater than 36 cents is 1.
(ii) To find the proportion of states with cigarette taxes greater than $1, you need to convert $1 into cents since the distribution is given in cents.
$1 is equivalent to 100 cents.
So, the proportion of states with cigarette taxes greater than $1 is the same as the proportion of states with cigarette taxes greater than 100 cents, which is (Max - 100) / 100. In this case, it would be (205 - 100) / 100 = 105 / 100 = 1.05, which can be treated as 1 as mentioned before.
Therefore, the proportion of states with cigarette taxes greater than $1 is also 1.