Question

the owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. let x represent the number of tickets bought in one purchase. the distribution for x is given in the table. what is the median of the distribution? 2 2.1 2.5 3

Explanation:

Step1: Calculate cumulative probabilities

Cumulative probability for \(X = 1\): \(P(X\leq1)=0.29\)
Cumulative probability for \(X = 2\): \(P(X\leq2)=0.29 + 0.44=0.73\)

Step2: Determine the median

The median \(M\) is the value such that \(P(X\leq M)\geq0.5\) and \(P(X\geq M)\geq0.5\). Since \(P(X\leq2) = 0.73\geq0.5\) and \(P(X\geq2)=1 - P(X\leq1)=1 - 0.29 = 0.71\geq0.5\)

Answer:

2