Suppose that 55% of adults with allergies report symptomatic relief with a speci

Question

Suppose that 55% of adults with allergies report symptomatic relief with a specific medication. If the medication is given to 10 patients with allergies,

a. What is the probability that the medicine is effective for exactly six patients?
b. What is the probability that the medicine is effective for at least one patient?
c. What is the probability that the medicine is effective for at most one patient?
d. What is the probability that the medicine is effective for exactly one patients?
e. Compute mean (or expected value), variance and standard deviation of the number patients for whom the medicine is effective in a sample of 10.

2 Suppose that 55% of adults with allergies report symptomatic relief with a specific medication. If the medication is given to 10 patients with allergies, a) What is the probability that the medicine is effective for exactly six patients? b) What is the probability that the medicine is effective for at least one patient? c) What is the probability that the medicine is effective for at most one patient? d) What is the probability that the medicine is effective for exactly one patients? e) Compute mean (or expected value), variance and standard deviation of the number patients for whom the medicine is effective in a sample of 10.

Explanation / Answer

This is binomial distribution with n=10 and p=0.55

P(x)=ncxp^x(1-p)^n-x

a. P(x=6)=0.2384

b. P(x>=1)=0.9997

c. P(x<=1)=0.0045

d. P(x=1)=0.0042

e. Mean=np= 5.5 and sd=sqrt(np(1-p))=1.57

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