Over a period of 12 years, there were approximately 2.42 shark attacks per year at the beaches in North Carolina.44 Consider the number of shark attacks during the thirteenth year.
a. What is the probability that there will be no shark attacks?
b. What is the probability that between two and five shark attacks inclusive will occur?
c. If there is evidence to suggest that the mean number of shark attacks per year has increased, the Coast Guard will begin more patrols to adequately protect the public. Suppose there are eight shark attacks in the thirteenth year. Is there evidence to suggest the need for more patrols? Justify your answer.
d. Find out exactly how many shark attacks there were in a recent year in North Carolina. Determine the probability of this occurrence.
e. Florida has the highest number of shark attacks per year, approximately 22.5, followed by Hawaii (4.33 per year), and California (3.17 per year). What is the probability that there will be no attacks in all four states in a given year?
In February 2013, the Chinese Ministry of Industry and Information Technology announced plans to expand broadband connections (or faster) to 70% of Chinese households.45 Suppose the plan is successful and 40 Chinese households are selected at random.
a. What is the probability that exactly 25 households have broadband coverage?
b. What is the probability that at most 30 households have broadband coverage?
c. What is the probability that more than 33 households have broadband coverage?
d. Suppose the number of households that have broadband coverage is within two standard deviations of the mean. What is the probability that the actual number that have broadband coverage is within one standard deviation of the mean?