Respuesta :
Answer:
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 = [tex]\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = 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([tex]\hat p[/tex] > 6%)
  P([tex]\hat p[/tex] > 6%) = P( [tex]\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex] > [tex]\frac{0.06 -0.08}{\sqrt{\frac{0.06(1- 0.06)}{644} } }[/tex] ) = 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.
