Question

A bottle maker believes that 23% of his bottles are defective.If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 602 bottles would differ from the population proportion by less than 4%? Round your answer to four decimal places.

Answer 1

Answer:

The appropriate answer is "0.9803".

Step-by-step explanation:

According to the question,

The probability of sample proportion differs from population proportion by les than 4% will be:

= $P(-\frac{0.04}{\sqrt{\frac{0.23\times 0.77}{602} } }<z<\frac{0.04}{\sqrt{\frac{0.23\times 0.77}{602} } } )$

= $P(-\frac{0.04}{\sqrt{\frac{0.1771}{602} } }<z<\frac{0.04}{\sqrt{\frac{0.1771}{602} } } )$

= $P(-2.33<z<2.33)$

= $0.9803$