ohducting an experiment designed identical treatment on 10 isolated coloniles of

Question

ohducting an experiment designed identical treatment on 10 isolated coloniles of the bacteria. The satisfactory if the mutation occurs in at least 8 of the colonies chance that his experiment will cause a gene mutation in a to produce a gene mutation in bacteria. The bacterial colony is 70%. He uses scientist considers his resuits 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 su ccess Explain why p (is the probability of success) is the same in every trial identify p(the probability of a success): (S points) the scientist will consider his results satisfactory? (Use a table or (5 points) b. What is the probability the formula). (1 point) What is the expected volue of mutated bacterial cultures in this sample? c. (2 p d. Fill in the blanks in the following sentence: "f the gene mutation experiment was repeated many times, each time sa isolated bacterial culturs, the average number of mutated cultures in a eated many times, each time using a sample of 20 approach_ Show your ow your work. Partial credit will be siven

Explanation / Answer

Problem # 1

1 . (a) Here a trial in this scenrio is gene mutattion in a bacteria.

(b) Here n is the number of times trial is performed, which is 10.

(c) Here "Success" is the successful gene mutation in bacteria in an individual trial.

(d) Here as the trial are independent and success probability is determiner by past precedence.

(e) Here success in any trial have probability is 0.7.

2.

Here results will be satisfactory. if X is the number of success ut of 10.

Pr(x < =8) = BIN(X < = 8 ; 10 ; 0.7) = 1 - BIN(X < = 7 ; 10 ; 0.7)

= 1 - 0.6172

= 0.3828

(3)

Expected value of mutated cultures = 10 * 0.7 = 7

(4)

Here the Fill in the blanks is 20 * 0.7 = 14

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