The opera theater manager calculates that 16%16% 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 592592 tickets would be less than 13%13%? Round your answer to four decimal places.

0.0228 = 2.28% probability that the proportion of tickets sold in a sample of 592 tickets would be less than 13%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For the sampling distribution of a sample proportion of size n, we have that

In this problem, we have that:

So

What is the probability that the proportion of tickets sold in a sample of 592 tickets would be less than 13%?

This is the pvalue of Z when X = 0.13. So

has a pvalue of 0.0228

0.0228 = 2.28% probability that the proportion of tickets sold in a sample of 592 tickets would be less than 13%

-232

step-by-step explanation:

x=6 and x=3

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