Question
1. An archer is able to hit the bull's eye 34% of the time. If she shoots 11 arrows, what is the probability that she
1. An archer is able to hit the bull's eye 34% of the time. If she shoots 11 arrows, what is the probability that she gets at least 2 bull's-eyes? Assume each shot is independent of the others. Express your answer as a percentage rounded to the nearest hundredth.
2. According to a college survey, 23% of all students work full-time. Find the mean for the number of students who work full time in samples of size 60 (rounded to the nearest hundredth).
3. According to a college survey, 11% of all students work full-time. Find the standard deviation for the number of students who work full time in samples of size 169 (rounded to the nearest hundredth).
4. A survey for brand recognition is done and it is determined that 66% of consumers have heard of Dull Computer Company. A survey of 16 randomly selected consumers is to be conducted. For such groups, would it be unusual to get 4 consumers who recognize the Dull Computer Company name? Why or why not? Explain your answer using descriptive statistics and/or probability appropriately. If your reasoning requires a z-score, enter the z-score rounded to the nearest hundredth. If your reasoning requires a probability, enter the probability as a decimal rounded to the nearest ten-thousandth.
5. A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.35. Find the probability that on a randomly selected trip, the number of whales seen is 4. Express your answer as a percentage rounded to the nearest hundredth.
6. Suppose the probability of contracting a certain disease is 1 in 54 for a new case in a given year. Approximate the probability that in a town of 120 people there will be at least one new case of the disease next year. Express your answer as a percentage rounded to the nearest hundredth without the % sign.