Elementary Statistics DepartmentalFinEm Part l(Form B) EmplID: Problem # 1 (12 p

Question

Elementary Statistics DepartmentalFinEm Part l(Form B) EmplID: Problem # 1 (12 points) A scientist is conducting an experiment designed to produce a gal colony is chance that his experiment will cause a gene mutation identical treatment on 12 isolated colonies of the bacteria. The gene mutation in bacteria. The in a bacterial colony is 80% He uses satisfactory if the mutation occurs in at least 10 of the colonies Let X be a random variabl e 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 a success): (5 points) What is the probability the scientist will consider his results satisfactory? (Use a table or the formula) b. (5 points) c. What is the expected value of mutated bacterial cultures in this sample? (1 point) d. Fill in the blanks in the following sentence: "If the gene mutation experiment was repeated many times, each time using a sample of 25 isolated bacterial cultures, the average number of mutated cultures in a sample would approach (1 point) Show your work. Partial credit will be given.

Explanation / Answer

a)
trial is treatment on 12 isolated colonies
n = 12 ,
success - cause a gene mutation in bacterial colony
p = 0.8 ,
b) P(X >= 10)
= 0.558345
c)
E(X) = np = 12 *0.8 = 9.6
d)
np = 25 * 0.8 = 20

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