A bottle maker believes that 11% 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 529529 bottles would be less than 9%9%

The value is  

Step-by-step explanation:

From the question we are told that

   The population proportion is  p =  0.11

   The sample size is n =  529

Generally given that the sample size is large enough (i.e n > 30), then the mean of this sampling distribution is mathematically represented as

Generally the standard deviation of this sampling distribution is

=>    

=>    

Generally the probability that the proportion of defective bottles in a sample of 529 bottles would be less than 9% (0.09) is mathematically represented as

Generally from the z table  the  area under the normal curve to the left corresponding to -1.47 is  

So

the graph on the bottom right