HELP!!! I extremely need help with the following questions, I am so confused and

Question

HELP!!! I extremely need help with the following questions, I am so confused and have no idea how to do it.

The HW is for Probability Theory class.

Would you also you show all the steps and do all the parts, please. Thank you.

3. Suppose that 80% of adults with allergies report symptomatic relief after they take a specific type of medication. Find the following probabilities. Be sure to give any calculator inputs used. [4 pts] a. If the medication is given to a random set of 25 new patients with allergies, what is the probability that the medicine is effective for 18 or more patients? [3 pts] b. What is the probability that in random set of 15 new patients with all patients find the medicine effective? ergies, exactly 7 13 pts] c. What is the probability that the researcher would finding 15 patients that found the medicine effective? need test 20 new patients before

Explanation / Answer

a) Mean = N*p = 25*0.8 = 20
SD = sqrt(N*p(1-p)) = 2

Z = (X - mean)/SD

P(X >= 18) = P(X > 17.5) = P(Z > (17.5-20)/2) = P(Z > -1.25) = 0.8944

b) Formula: P(X = k) = nck * pk * (1-p)(n-k)

P(X = 7) = 15c7 * 0.87 * 0.28 = 0.0034548

c) P(X = 15) = 20c15 * 0.815 * 0.25 = 0.1746

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