Question

A prescription drug manufacturer claims that only 10% of all new drugs that are shown to be effective in animal tests ever pass through all the additional testing required to be marketed. The manufacturer currently has eight new drugs that have been shown to be effective in animal tests, and they await further testing and approval. You are not allowed to use PHStat4 for this question. Show your calculations clearly by labeling them properly so that it is clear to infer what the calculations are for

a. Find the probability that none of the drugs is marketed.

b. Find the probability that at least 2 are marketed.

c. Find the expected number of marketed drugs among the eight.

Answer 1

Solution:

Given:  A prescription drug manufacturer claims that only 10% of all new drugs that are shown to be effective in animal tests ever pass through all the additional testing required to be marketed.

p = probability of all new drugs that are shown to be effective in animal tests ever pass through all the additional testing required to be marketed

p = 0.10

n = Number of new drugs that have been shown to be effective in animal tests, and they await further testing and approval

n = 8

x = Number of new drugs that are shown to be effective in animal tests ever pass through all the additional testing required to be marketed follows a Binomial distribution with parameters n =8 and p = 0.10

Binomial probability formula :

Where q = 1 – p = 1 - 0.10 = 0.90

Part a) Find:

P( None of the drugs is marketed ) =.........?

P( X = 0 ) =............?

Part b)

P( at least 2 are marketed )=..........?

Find:

P(X = 0) and P(X = 1)

We have:

Now find: P(X = 1)=.......?

Thus

Part c) Find the expected number of marketed drugs among the eight.