3 and 4

3. Left-Handedness According to data from the American Medical Association, 10% of us are left-handed. a. If three people are randomly selected, find the probability that they are all left-handed. b. If three people are randomly selected, find the probability that at least one of them is left-handed. continued 280 CHAPTER 6 Normal Probability Distributions c. Why can't we solve the problem in part (b) by using the normal approximation to the bino- mial distribution? d. If groups of 50 people are randomly selected, what is the mean number of left-handed peo- ple in such groups? e. If groups of 50 people are randomly selected, what is the standard deviation for the numbers of left-handed people in such groups? f. Use the range rule of thumb to determine whether 8 left-handed people is a significantly high number of left-handed people in a randomly selected group of 50 people. 4. Blue Eyes Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University). a. Let B denote the event of selecting someone who has blue eyes. What does the event B denote? b. Find the value of P(B). C. Find the probability of randomly selecting three different people and finding that all of them have blue eyes. d. Find the probability that among 100 randomly selected people, at least 45 havJ blue eyes. e. If 35% of us really do have blue eyes, is a result of 45 people with blue eyes among 100 ran- domly selected people a result that is significantly high? 5. Foot Lengths of Women Assume that foot lengths of with a mean of 9.6 in, an