There is some evidence to suggest that businesses are moving out of states where unions are prevalent. In California, 18.4% of all workers belong to a union, and in Arkansas, 3.7%.24 Suppose 20 workers from California and 20 workers from Arkansas are selected at random.
a. Find the probability that at most two California workers belong to a union.
b. Find the probability that none of the Arkansas workers belongs to a union.
c. Find the probability that at least one worker from each state belongs to a union.
A recent report suggests that one-third of all U.S. children are overweight or obese. One possible cause is the availability of junk foods and sugary snacks in schools. Approximately 40% of all students buy and eat one or more snacks at school.25 Suppose 40 school children are selected at random.
a. Find the mean, variance, and standard deviation of the number of school children (out of the 40 selected) who buy and eat a snack at school.
b. Construct intervals one, two, and three standard deviations from the mean.
c. Suppose 27 students (out of the 40 selected) buy and eat a snack at school. How many standard deviations from the mean is this observation? What does this distance measure indicate about the likelihood of observing 27 students who buy and eat a snack at school?