Ascientist is conducting an experiment designed to produce a gene mutation in bacteria. the chance that his experiment will cause a gene mutation in a bacterial colony is 70%. he uses identical treatment on 10 isolated colonies of the bacteria. the scientist considers his results satisfactory if the mutation occurs in at least 8 of the colonies.

let x be a random variable representing the number of bacterial colonies that have mutated.

a.) explain why x is a binomial random variable:
-specify, in words, what is a trial in this scenario
-identify n (the number of trials)
-specify, in words, which outcome of a trial would be defined as a "success"
-explain why p (is the probability of success) is the same in every trial
-identify p (the probability of success)

b.) what is the probability the scientist will consider his results satisfactory?

c.) what is the expected value of mutated bacterial culture in this sample?

d.) fill in the blanks of the following sentence:
"if the gene mutation experiment was repeated many times, each time using a sample of 20 isolated bacterial cultures, the average number of mutated cultures in a sample would approach "