A bottle maker assumes that 24% of his bottles are defective. If the bottle maker is right, what is the probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4%? Round your answer to four decimal places.

The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.What is the probability that the population proportion will be greater than 4%?To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation. Here is the formula:z = (x-μ)/σFirst population proportion = 0.24The sample proportion, hat p = 0.04​Z score = [tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]So, the Z score will = -10.9469So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469,  is = 10.9069Learn more about the z score here:https://brainly.com/question/25638875#SPJ1