United Medicine Inc claims that a drug Viro significantly re

United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 75 percent of all patients. Suppose that this drug is given to 12 randomly selected patients who have been diagnosed with the viral infection.

Let x equal the number of the 12 randomly selected patients whose symptoms are significantly relieved. What distribution describes the random variable x ? (Round your answers to 1 decimal place.)

Assuming that the company\'s claim is correct, find P(x 9). (Round your answer to 4 decimal places.)

Suppose that of the 12 randomly selected patients, 9 have had their symptoms significantly relieved by Viro. Based on the probability in part b, would you believe the claim of United Medicine, Inc.?

; The probability of 9 or fewer being relieved is .

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
n = 12, p = 0.75

b)
P( X < = 9) = P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 12 9 ) * 0.75^9 * ( 1- 0.75 ) ^3 + ( 12 8 ) * 0.75^8 * ( 1- 0.75 ) ^4 + ( 12 7 ) * 0.75^7 * ( 1- 0.75 ) ^5 + ( 12 6 ) * 0.75^6 * ( 1- 0.75 ) ^6 + ( 12 5 ) * 0.75^5 * ( 1- 0.75 ) ^7 + ( 12 4 ) * 0.75^4 * ( 1- 0.75 ) ^8 + ( 12 3 ) * 0.75^3 * ( 1- 0.75 ) ^9 + ( 12 2 ) * 0.75^2 * ( 1- 0.75 ) ^10 + ( 12 1 ) * 0.75^1 * ( 1- 0.75 ) ^11 + ( 12 0 ) * 0.75^0 * ( 1- 0.75 ) ^12
= 0.6093

c)
No, as th eproportion rate is lower to the proportion stated, 75%.