Question

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 support trained?

Give your answer to four decimal places.

Answer: _________

Answer 1

Solution:- The probability that less than 6% of the dogs are emotional support trained is 0.0021.

P = 0.23, n = 50

$\hat{p}=0.06$

By applying normal distribution:-

$z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

z = -2.856

P(z < - 2.856) = 0.0021