ementary Statistics Departmental Final Exam Part I (Form A) EmplD: d. The equati

Question

ementary Statistics Departmental Final Exam Part I (Form A) EmplD: d. The equation of the Least Squares Regression (LSR) Line is: ourly Wa (2 point Elementary Statistics Departmental Final Exam Part lI ( Form A) EmplID Problem # 1 (12 points) A scientist 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 r a Stat 3 points Explain why X is a binomial random variable a. 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 a success): . (S points) b. What is the probability the scientist will consider his results satisfactory? (Use a table or (5 points) the formula) What is the expected value of mutated bacterial cultures in this sample? c. (1 point) d. Fill in the blanks in the following sentence: "If the gene mutation experiment was repeated many times, each time using a isolated bacterial cultures, the a approach sample of 20 verage number of mutated cultures in a sample would (1 point) Show your work. Partial credit will be given

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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