Question

9. A father asks his sons to cut their backyard lawn. Since he does not specify which of his three sons is to do the job, each boy tosses an unbiased coin to determine the odd person, who must then cut the lawn. In the case that all three get heads or tails, they continue tossing until they reach a decision. What is the minimum number of tosses required to reach a decision with probability 0.957 10. The time between the first and second heart attacks for a certain group of people is an exponential random variable. If 40% of those who have had a heart attack will have another one within the next five years, then what is the probability that a person who had one heart attack five years ago will not have another one in the next five years? 11. By determining the value(s) of k for which the following is a density function 12. An experimenter is interested in the hypothesis testing problem Ho: μ = 10 mm versus Hajl # 10 mm, where u is the average thickness of a set of plywood sheets. Suppose that a sample of 16 sheets obtained and their thickness is measured. Let the sample mean is 10.61355 mm and sample variance is 1.96 sq mm. Assume normality, determine the P-value of the test.

Answer 1

9)

One way you could solve this one is using the binomial distribution method. Remember that this is used to calculate the probability of successes or failures. The possibilities are {HHH,HHT,HTH,THH,TTH,THT,HTT,TTT}. Of these 8 possibilies, 6 yield a success (where a success is a son being chosen). Probability of a success is 3/4, failure is 1/4. So, now you can simply use the binomial distribution for it taking only 1 group of tosses, 2, 3, and 4 to get the answer using:

binx, p

where p is the probability of success, q the probability of failure, x is the number of successes you want, n is the total number of trials. Just to make sure that's clear, here's an example.

If I want to find the probability of it taking only 3 tosses to get 1 success, then:

3 (3/4)' (1/4)21406