Question

In: Statistics and Probability

A bottle maker calculates that13% of his bottles are defective. If the bottle maker is accurate,...

A bottle maker calculates that13% 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 454 bottles would be less than 12%? Round your answer to four decimal places.

Solutions

Expert Solution

Solution

Given that,

p = 0.13

1 - p = 1-0.13=0.87

n = 454

= p =0.13

=  [p ( 1 - p ) / n] =   [(0.13*0.87) /454 ] = 0.0158

P( <0.12 ) =

= P[( - ) / < (0.12-0.13) / 0.0158 ]

= P(z < -0.63)

Using z table,   

=0.2643

probability=0.2643

orchestra answered 2 years ago
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