The Ventura County Star (June 20, 2012) reported on a study of children in public schools in California that looked at the proportion of overweight or obese children. In Huntington Park (a small city outside Los Angeles), 53% of the children were overweight or obese; this was the highest rate found in any city in California. Suppose a random sample of 200 public school children is taken from Huntington Park. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of overweight/obese children in the sample will be greater than 0.50.
a. Without doing any calculations, determine whether this probability is greater than 50% or if it is less than 50%. Explain.
b. Calculate the probability that 50% or more are overweight or obese.