Hey guys Please help me with this statistics questions It wo

Hey guys. Please help me with this statistics questions. It would be great if someone could show me step by step on how to get to answers. Deeply appreciated. THANKS!

4. In each situation below, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. a. An auto manufacture chooses one car from each hour\'s production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, etc...) in the car\'s paint. b. The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty; X is the number who say \"Yes.\" c. Joe buys a ticket in his state\'s \"Pick 3\" lottery game every week; X is the number of times in a year that he wins a prize.

Solution

a) Not binomial as there are no independent and identical bernoulli trials here.

b) This is binomial as the number of people is sum of bernoulli trials, each person is either says Yes or not, and these persons are independent of one another

c) This is binomial as the total number of won lotteries is is of independent bernoulli tirials as each week either he wins the lottery or not, and outcome in every week is independent of other weeks.