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In: Statistics and Probability

A researcher believes that 8% of pet dogs in Europe are Labradors. If the researcher is...

A researcher believes that 8% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 594 pet dogs would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

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Expert Solution

Solution

Given that,

p = 0.08

1 - p = 1 0.08 = 0.92

n = 594

= p = 0.08

=  p ( 1 - p ) / n

=   (0.08 * 0.92) / 594 = 0.01113

1 - P(0.05 < < 0.11) = 1 - P( (0.05 - 0.08) / 0.01113 < ( - ) / < (0.11 - 0.08) / 0.01113)

= 1 - P(-2.695 < z < 2.695)

= 1 - [P(z < 2.695) - P(z < -2.695)]

= 1 - [0.9965 - 0.0035]

= 1 - 0.993

= 0.0070

Probability = 0.0070

orchestra answered 2 years ago
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