Question

The probability that a person suffers from migraine has relief with a specific drug is 0.9, three people are randomly selected with migraine to which the drug is administered. Find the probability that the number of people achieving relief will be:
a) Does it meet the characteristics of a binomial variable? Yes or no,
b) No person
c) Exactly 1
d) More than one
e) Two or less
f) Two or three
g) At least 3
h) What is the expected value of the number of people achieving relief in the sample and what is their standard deviation?
Answers yes, 0.001, 0.027, 0.972, 0.271, 0.972 0.729, 2.7 expected value and standard deviation is 0.5196

Answer 1

(a)

Yes

It meets the characteristics of a binomial distribution

Explanation:

(i) The experiment consists of n = 3 identical trials

(ii) Each trial consists of in one of two outcomes: Achieving relief & Not achieving relief

(iii) The probability of success , p = 0.9 remains the same from trial to trial

(iv) The n =3 trials are independent

(b)

n = 3

p =0.9

q = 1 - p = 0.1

(c)

(d)

P(X>1)=P(X=2) +P(X=3)

So,

P(X>1)=0.243 +0.729 = 0.972

So,

Answer is:

0.972

(e)
P(P(X2) =P(X = 2)+ P(X = 1) +P(X = 0)

So,

P(X2) = 0.243 + 0.027 +0.001 = 0.271

So,

Answer is:

0.271

(f)

P(X = 2 OR 3) = P(X=2) +P(X =3)

So,

P(X = 2 OR 3) = 0.243 + 0.729 = 0.972

So,

Answer is:

0.972

(g)

P(X At least 3)= P(X = 3)

So,

P(At least 3)= 0.729

So,

Answer is:

0.729

(h)

(i) Expected Value = (X) =op = 3 X0.9 = 2.7

So,

Answer is:

2.7

(ii) Standard deviation =

So,

Answer is:

0.5196