Question

If you wanted to make a game where you pay $5 if you can't guess a random dogs weight within 16lbs what payout should you offer you make the game zero-expected value

Answer 1

Following are the solution to the given question:

Explanation:

The population std. dev of the dog weight=8

`\sigma=8\\\\P(\text{guess with in 16 lbs}) = P(|X-\mu|\leq 16)\\\\=P(-2 \leq Z \leq 2) = 0.9544\\\\`

Calculating the payout w s.t:

`E[netpay]=0=(-5) * 0.9544+w* (1-0.9544)\\\\ w =(5 * (0.9544)/(1-0.9544)) =\$ 104.65`

therefore, we assume that the weight of the dog is a normal distribution with std. deviation that is 8.