- The length of pregnancy for a randomly selected pregnant sheep is \(D\) days where
$$D \sim \mathrm {~N} \left( 112.4 , \sigma ^ { 2 } \right)$$
Given that 5\% of pregnant sheep have a length of pregnancy of less than 108 days,
- find the value of \(\sigma\)
Qiang selects 25 pregnant sheep at random from a large flock.
- Find the probability that more than 3 of these pregnant sheep have a length of pregnancy of less than 108 days.
Charlie takes 200 random samples of 25 pregnant sheep.
- Use a Poisson approximation to estimate the probability that at least 2 of the samples have more than 3 pregnant sheep with a length of pregnancy of less than 108 days.