Question

stion yet vered ts out of The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plans on showcasing a-simple random sample of its dogs in a show. Depending on which dogs are chosen, the proportion of emotional support trained dogs may vary. In a sample of 50 dogs, what is the probability that less than 6% of the dogs are emotional s trained? Give your answer to four decimal places Flag stion Answer:

Answer 1

Since a sample of 50 is taken hence Z statistic is applicable here to find the probability for less than 6 % of the dogs are emotionally trained.

Hence Z formula

$Z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n}}}$

Here

$\hat{P}=0.06$

n=59 and P = 0.23

Hence by calculation we get Z=-2.856

To find probability for less than 6% we find P(Z<-2.856) Using Z statistic table shown below

P(Z<-2.856)=0.0021