7.3 Exercise 47

Use the following to answer the next two exercises: The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations.

Suppose in a local kindergarten through 12^th grade (K–12) school district, 53 percent of the population favor a charter school for grades K through five. A simple random sample of 300 is surveyed. Calculate the following using the normal approximation to the binomial distribtion.

1. Find the probability that less than 100 favor a charter school for grades K through 5.
2. Find the probability that 170 or more favor a charter school for grades K through 5.
3. Find the probability that no more than 140 favor a charter school for grades K through 5.
4. Find the probability that there are fewer than 130 that favor a charter school for grades K through 5.
5. Find the probability that exactly 150 favor a charter school for grades K through 5.

If you have access to an appropriate calculator or computer software, try calculating these probabilities using the technology.