Question

Male border collies tend to weight more than females. Can we use weight to predict whether a border collie is male or female? Suppose that the weights of fully-grown female border collies follow a normal distribution with mean 15 kilograms and SD 3 kilograms. Suppose also that the weights of fully-grown male border collies follow a normal distribution with mean 21 kilograms and SD 4 kilograms.

1. Determine the probability that this prediction rule would mistakenly predict that a female border collie is male. (In other words, determine the proportion of female border collies that weigh more than 18 kilograms.)

2. Determine the probability that this prediction rule would mistakenly predict that a male border collie is female. (In other words, determine the proportion of male border collies that weigh less than 18 kilograms.)

3. Assume we need a new cutoff value that is greater than 18 kilogram to decrease the probability that we would mistakenly predict a female border collie to be male, find the new cut-off value needed in order that only 5% of female border collies are mistakenly predicted to be male.

please draw a graph to indicate your work and full step on the formula, THANK YOU.

Answer 1