Some biologists believe the evolution of handedness is linked to complex behaviors such as tool-use. Under this theory, handedness would be genetically passed on from parents to children. That is, left-handed parents would be more likely to have left-handed children than right-handed parents. An alternate theory asserts that handedness should be random, with left- and right-handedness equally likely. In a recent study using a simple random sample of n = 76 right-handed parents, 50 of the children born were right-handed. (p = 0.658.) Suppose handedness is a random occurrence with either hand equally likely to be dominant, implying that the probability of a right-handed offspring is π = 0.50.
a) Show that it is reasonable to approximate the sampling distribution of p using a normal distribution.
b) Assuming left- and right-handed children are equally likely from right-handed parents, what is the probability of observing a sample proportion of at least p = 0.658?

Question

Some biologists believe the evolution of handedness is linked to complex behaviors such as tool-use. Under this theory, handedness would be genetically passed on from parents to children. That is, left-handed parents would be more likely to have left-handed children than right-handed parents. An alternate theory asserts that handedness should be random, with left- and right-handedness equally likely. In a recent study using a simple random sample of n = 76 right-handed parents, 50 of the children born were right-handed. (p = 0.658.) Suppose handedness is a random occurrence with either hand equally likely to be dominant, implying that the probability of a right-handed offspring is π = 0.50. 
a) Show that it is reasonable to approximate the sampling distribution of p using a normal distribution. 
b) Assuming left- and right-handed children are equally likely from right-handed parents, what is the probability of observing a sample proportion of at least p = 0.658?

Quizplus · Accepted Answer

The Answer of Some biologists believe the evolution of handedness is linked to complex behaviors such as tool-use. Under this theory, handedness would be genetically passed on from parents to children. That is, left-handed parents would be more likely to have left-handed children than right-handed parents. An alternate theory asserts that handedness should be random, with left- and right-handedness equally likely. In a recent study using a simple random sample of n = 76 right-handed parents, 50 of the children born were right-handed. (p = 0.658.) Suppose handedness is a random occurrence with either hand equally likely to be dominant, implying that the probability of a right-handed offspring is π = 0.50. 
a) Show that it is reasonable to approximate the sampling distribution of p using a normal distribution. 
b) Assuming left- and right-handed children are equally likely from right-handed parents, what is the probability of observing a sample proportion of at least p = 0.658?

Some Biologists Believe the Evolution of Handedness Is Linked to Complex