Use the following information to answer questions 1-3. Alex tracked how many cups of coffee he drank each day for a month and then compiled the results into a probability distribution, as shown below Number of Cups of Coffee X 13 Relative Frequency, P(X) 0.0240423 0.2910.1720.090 calculate the IQR of Alex’s probability distribution
To find the IQR, we first need to find the first quartile (Q1) and third quartile (Q3).
To find Q1, we need to find the cumulative relative frequency that is closest to 0.25.
Starting from the smallest value of X and adding up the relative frequencies, we can see that the cumulative relative frequency closest to 0.25 is 0.0240423 + 0.291 = 0.3150423.
Looking at the probability distribution, we can see that the corresponding value of X for this cumulative relative frequency is 1 cup of coffee. Therefore, Q1 = 1.
To find Q3, we need to find the cumulative relative frequency that is closest to 0.75.
Starting from the largest value of X and working backwards, we can see that the cumulative relative frequency closest to 0.75 is 1.0 - 0.172 - 0.090 = 0.738.
Looking at the probability distribution, we can see that the corresponding value of X for this cumulative relative frequency is 3 cups of coffee. Therefore, Q3 = 3.
Now that we have found Q1 and Q3, we can calculate the IQR as Q3 - Q1 = 3 - 1 = 2.
Therefore, the IQR of Alex's probability distribution is 2.