Question

9. The four conditions required for using a Binomial distribution are. (a) A fixed number of trials (n). b) On each trial, there are two possible outcomes, one of which we call a "success" (c) On each trial, P(success) is the same (d) The outcomes of each trial are independent For each of the following decide if the random variable defined (X) is a Binomial variable or not. If it is not a Binomial variable, say which of the four conditions are not met. If it is a Binomial, give the probability function substituting in the values for n and T given by the question (a) A box contains 100 batteries. Ten of the batteries are dead. Five batteries are randomly selected (simultaneously sampling 5 is the same as sampling one-by-one without replacement). Define X as the number of dead batteries in the sample. (b) In a large population 5% of the people are unemployed. We randomly select 10 people. Define X as the number of employed people in the sample. When the question says "large population" this means that there is very little difference between sampling with and without replacement. So even though sampling 10 people is the same as sampling one-by-one without replacement, we can treat the situation as if it were sampling with replacement (c) In a large population of married couples (husbands and wives) 5% all people are unemployed. We randomly select 5 couples (husbands and wives). Define X as the number of unemployed people in the 10 people sampled. (d) Roll a six-sided die repeatedly until it comes up 5. Defined X as the total number of rolls

Answer 1