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. which is the correct interpretation of the standard deviation? the number of tickets purchased typically varies from the expected value by 0.95 tickets. if many, many purchases are made, the expected number of tickets purchased is 2.1. the mean number of tickets purchased typically varies from the expected value by 0.95 tickets. the mean number of tickets purchased typically varies from the expected value by 0.89 tickets.

Explanation:

The standard deviation measures the typical amount by which individual data points (in this case, the number of tickets purchased in each transaction) deviate from the mean (expected value). The first option correctly states that the number of tickets purchased (the data point \(X\)) typically varies from the expected value by the standard - deviation amount. The second option is about the expected value (mean) itself, not the standard deviation. The third option incorrectly refers to the mean (which is a single value) varying, when it is the individual data points (\(X\)) that vary.

Answer:

The number of tickets purchased typically varies from the expected value by 0.95 tickets.