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 644 pet dogs would be greater than 6%? Round your answer to four decimal places.

Proportion of Labradors in a sample of 644 pet dogs would be greater than 6% is 0.9838.

Step-by-step explanation:

We are given that a researcher believes that 8% of pet dogs in Europe are Labradors.

We have to find the probability that the proportion of Labradors in a sample of 644 pet dogs would be greater than 6%.

Let p = % of pet dogs in Europe that are Labradors = 8%

The z score probability distribution is given by;

                 Z = ~ N(0,1)

where, = sample proportion of Labradors

            n = sample of pet dogs = 644

So, probability that the proportion of Labradors in a sample of 644 pet dogs would be greater than 6% is given by = P( > 6%)

    P( > 6%) = P( > ) = P(Z > -2.14)

                    = P(Z < 2.14) = 0.9838  {using z table directly}

Hence, the probability that the proportion of Labradors in a sample of 644 pet dogs would be greater than 6% is 0.9838.

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step-by-step explanation: