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

Answer:

Following are the solution to the given question:

Step-by-step 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:

$E[netpay]=0=(-5) \times 0.9544+w\times (1-0.9544)\\\\ w =(5 \times \frac{0.9544}{1-0.9544}) =\ 104.65$

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