the Ladies Home Journal claim? Calculate anprobability to support your answer.appropriate T6.12. Ladies Home Journal magazine reported that 66%of all dog owners greet their dog before greeting theirspouse or children when they return home at the end ofthe workday. Assume that this claim is true. Suppose 12dog owners are selected at random. Let X = the number ofowners who greet their dogs first.(a) Explain why X is a binomial random variable.(b) Only 4 of the owners in the random sample greetedtheir dogs first. Does this give convincing evidence against

T6.12. The random variable X is defined as the number of owners who greet their dogs first. The sample size is 12, and 66% of all dog owners greet their dog before greeting their spouse or children when they return home at the end of the workday.(a) Conditions of binomial distribution: The variable defined in the experiment must have only two possible outcomes, ‘success, failure’ which are mutually exclusive. In the experiment the total number of trails must be fixed and are known in advance. For each and every trail in the experiment the probability of success is same or remains constant. In each trail the outcomes of variable are independent of each other. Explanation: The variable defined in the study is 'greets their dogs first or not' which are two possible outcomes 'greets first, not greets first'. The total number of dog owners are 12, that is the number of trails is fixed and known in advance. The probability of dog owners who greets their dogs first is 0.66 and is constant for all trails. The each dog owner is independent to each other. Since all the conditions are satisfied indicating that the variable X follows binomial distribution. Thus, the variable X is a binomial random variable.(b) The probability that exactly 4 dog owners who greet their dogs first is, PX=4=1240.6641-0.6612-4=495×0.18974736×0.0001785793904896=0.0168 Thus, the probability that exactly 4 dog owners who greet their dogs first is 0.0168. The probability value is 0.0168 which is less than 0.05(general level of significance) indicating that the convincing evidence against the Ladies Home Journal claim.