Homework 9

1.  An archer is able to hit the bull’s-eye 27% of the time. If she shoots 11 arrows, what is the probability that she does not get exactly 4 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, 55% of all students work full time. Find the mean for the number of students who work full time in samples of size 112 (rounded to the nearest hundredth).

3.  According to a college survey, 55% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 253 (rounded to the nearest hundredth).

4.   A survey for brand recognition is done and it is determined that 36% 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 significantly high to get 2 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.   The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.8. Find the probability that in a randomly selected year, the number of lightning strikes is 3. Express your answer as a percentage rounded to the nearest hundredth.

6.  Suppose the probability of a major earthquake on a given day is 1 out of 656. Approximate the probability that there will be at least one major earthquake in the next 1,624 days. Express your answer as a percentage rounded to the nearest hundredth without the % sign.