Question

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 503 pet dogs would be greater than 11%? Round your answer to four decimal places.

Answer 1

Solution:

We are given

Population proportion = p = 0.08

So, q = 1 – p = 1 – 0.08 = 0.92

Sample size = n = 503

Sample proportion = P = 0.11

We have to find P(P>0.11)

P(P>0.11) = 1 – P(P<0.11)

Z = (P – p)/sqrt(pq/n)

Z = (0.11 – 0.08)/sqrt(0.08*0.92/503)

Z = 0.03/ 0.012096

Z = 2.480159

P(Z<2.480159) = P(P<0.11) = 0.993434

(by using z-table/excel)

P(P>0.11) = 1 – P(P<0.11)

P(P>0.11) = 1 – 0.993434

P(P>0.11) = 0.006566

Required probability = 0.0066