Problem 1BSC

Notation In a clinical trial of the cholesterol drug Lipitor, 270 subjects were given a placebo, and 7% of them developed headaches. For such randomly selected groups of 270 subjects given a placebo, identify the values of n, p, and q that would be used for finding the mean and standard deviation for the number of subjects who develop headaches.

Problem 1BSC

Answer:

Step1 of 2:

We have In a clinical trial of the cholesterol drug Lipitor, 270 subjects were given a placebo, and 7% of them developed headaches. For such randomly selected groups of 270 subjects given a placebo,we need to identify the values of n, p, and q that would be used for finding the mean and standard deviation for the number of subjects who develop headaches.

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 270 and p = 0.07.

q = 1 - p

= 1 - 0.07.

= 0.93

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

With mean E(x) = np and variance var(x) = npq

Consider,

E(x) = np

= 2700.07

= 18.9

Therefore,E(x) = 18.9

var(x) = npq

= 2700.070.93

= 17.577

Step2 of 2:

Standard deviation is given by =

=

= 4.1924.

4 people.