Historically, 74% of credit card users carry a balance from month-to-month. A certain credit card company would like to study the spending patterns of its cardholders in more detail and to start the analysis, takes a random sample of 140 cardholders. What is the probability more than 72% of these cardholders are carrying a balance

The probability more than 72% of the cardholders are carrying a balance is 0.2946

Explanation:

Test statistic (z) = (p' - p) : sqrt[p (1-p) : n]

p' is the sample proportion = 0.72

p is the population proportion = 0.74

n is the number of cardholders sampled = 140

z = (0.72 - 0.74) : sqrt[0.74 (1-0.74) : 140] = - 0.02 : 0.037 = - 0.54

The cumulative area of the test statistic is the probability that less than 72% of the cardholders are carrying a balance. The probability is 0.7054.

Probability (more than 72% of the cardholders are carrying a balance) = 1 - 0.7054 = 0.2946