Question

1. The probability of success for a new experimental treatment is 0.80 in women.  Assuming the same probability of success applies to men, a new trial is conducted to test the treatment in a sample of 6 men.  Note that this defines a binomial random variable.

1. What is the minimum number of possible successes?
2. What is the maximum number of possible successes?
3. What is the expected number of successes? Report to one decimal place, such as 1.2.

2. Continuing from the previous question where the probability of success is 0.80, what is the probability of observing exactly 6 successful treatments in your sample of 6 men?

		0.26
		4.8
		0.015
		0.026

3. Continuing from the previous question where the probability of success is 0.80, what is the probability of observing less than 6 successful treatments in your sample of 6 men? (hint: the answer is a natural extension of the answer from the previous question)

		0.74
		0.26
		0.15
		1.0

Answer 1

Solution:

Given:

p = probability  of success =  0.80

n = Number of men = 6

x = Number of successful treatments in sample of 6 men follows a Binomial distribution with parameters n = 6 and p = 0.80

Part 1)

Binomial Random variable x can take values from 0 to n.

i) the minimum number of possible successes = 0

ii)  the maximum number of possible successes = n = 6

iii)  the expected number of successes = n * p = 6 * 0.8 = 4.8

Part 2) Find the probability of observing exactly 6 successful treatments in your sample of 6 men.

P( X= 6) =............?

Binomial probability formula :

Where q = 1 – p = 1 - 0.80= 0.20

Thus

Thus correct answer is: 0.26

Part 3) Find  the probability of observing less than 6 successful treatments in your sample of 6 men.

P( X< 6) = ..............?

P( X< 6) = 1 - P( X = 6)

P( X< 6) = 1 - 0.26

P( X< 6) = 0.74

Thus correct answer is: 0.74