FInd mean standard deviation probability A to E 3 Five of t

FInd mean & standard deviation, probability A to E

3. Five of the 20 drugs went on to be declared high potential. Historically, French has found 15% of the drugs under \'\'Hi-Po\'\' development to secure FDA approval. a. What is the mean & standard deviation for the number of drugs to receive FDA approval? b. What is the probability that no drugs receive approval? c. What is the probability that 1 drug receives approval? d. What s the probability that multiple drugs receive approval? e. Taking a drug through this process costs $125 million and a successful bring in $1 billion, estimate the mean and standard deviation for French?s net revenue.

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)
Mean ( np ) =20 * 0.15 = 3
Standard Deviation ( npq )= 20*0.15*0.85 = 1.5969

b)
P( X = 0 ) = ( 20 0 ) * ( 0.15^0) * ( 1 - 0.15 )^20
= 0.0388

c)
P( X = 1 ) = ( 20 1 ) * ( 0.15^1) * ( 1 - 0.15 )^19
= 0.1368

d)

P( X < 2) = P(X=1) + P(X=0) +
= ( 20 1 ) * 0.15^1 * ( 1- 0.15 ) ^19 + ( 20 0 ) * 0.15^0 * ( 1- 0.15 ) ^20 +   
= 0.1756

P( X > = 2 ) = 1 - P( X < 2) = 0.8244