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

The appropriate answer is "0.9803".

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{(0.23* 0.77)/(602) } }<z<\frac{0.04}{\sqrt{(0.23* 0.77)/(602) } } )`

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

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

=
`0.9803`