A Six Flags Great Adventure Theme Park now offers a “wild safari” drive-thru with more than 1000 animals roaming freely on over 400 acres. The park claims that the probability of some car damage by an animal during a safari drive-thru is 0.60. Suppose 20 cars are selected at random.
a. Find the probability that exactly 10 cars will be damaged.
b. Find the probability that at least 15 cars will be damaged.
c. Find the probability that no more than 12 cars will be damaged.
d. Suppose 19 cars are damaged. Is there any evidence to suggest the claim of 0.60 is false? Justify your answer. Write a Solution Trail for this problem.
Parents tend to be very good at diagnosing their children’s routine medical problems, such as an ear infection, sinus infection, or strep throat. If an ailment is identified correctly, a trip to the doctor’s office may be avoided. A physician may confer with a parent by telephone, and simply call a pharmacy with a prescription for an antibiotic. Suppose parents are correct 90% of the time, and 50 families with a child suffering from some minor illness are selected at random.
a. Find the mean, variance, and standard deviation of the number of parents who identify their child’s illness correctly.
b. Find the probability that at least 42 parents are correct.
c. Find the probability that between 42 and 47 (inclusive) parents are correct.
d. Suppose 41 parents are actually correct. Is there any evidence to suggest that fewer than 90% of parents are correct? Justify your answer.
A building inspector enforces building, electrical, mechanical, plumbing, and energy code requirements for the safety and health of people in a certain city, county, or state. In Santa Cruz County, the probability that a building inspector will find at least one code violation at a commercial building is 0.25. Suppose 30 commercial buildings are selected at random.
a. Find the mean, variance, and standard deviation of the number of commercial buildings with at least one violation.
b. Find the probability that the number of commercial buildings with at least one violation will be within one standard deviation of the mean.
c. Find the probability that the number of commercial buildings with at least one violation will be more than two standard deviations from the mean.
d. Suppose the actual number of commercial buildings with at least one violation is 10. Is there any evidence to suggest that code violations are found in more than 25% of commercial buildings? Justify your answer.