Question

The opera theater manager assumes that 26% of the opera tickets for tonight's show have been sold. if the manager is correct, what is the probability that the proportion of tickets sold in a sample of 811 tickets would differ from the population proportion by less than 4% ? round your answer to four decimal places?

Answer 1

To find the probability that the proportion of tickets sold in a sample of 811 tickets would differ from the population proportion by less than 4%, we calculate the standard deviation and then use the standard normal distribution table to find the probability.

Step-by-step explanation:

To find the probability that the proportion of tickets sold in a sample of 811 tickets would differ from the population proportion by less than 4%, we can use the standard deviation formula for proportions, given by o = sqrt(npq). Here, n is the sample size (811), p is the assumed population proportion (0.26), and q is 1 - p (0.74). Plugging in these values, we get o = sqrt(811 * 0.26 * 0.74) = 13.23.

To find the probability, we need to calculate the z-score for a 4% difference, which is given by (0.04 - 0) / 0.01323 = 3.026. Using a standard normal distribution table, we can find that the probability of a z-score less than 3.026 is 0.9987.

Therefore, the probability that the proportion of tickets sold in a sample of 811 tickets would differ from the population proportion by less than 4% is approximately 0.9987.