For the population of people who suffer occasionally from mi

For the population of people who suffer occasionally from migraine headaches, suppose p = 0.80 is the proportion who get some relief from taking a certain medicine. For a particular subject, let x = 1 if they get relief and x = 0 if they do not. For a random sample of 20 people who suffer from migraines, answer the following questions. a. State the probability distribution for each observation. Choose the sentence below that best describes the probability distribution. Find the mean of the sampling distribution of the sample proportion who get relief. Find the standard deviation of the sampling distribution of the sample proportion. Explain what the standard deviation in part (c) describes. Choose the sentence below that best describes the standard deviation.

Solution

a)
Option B
Because it gives the explanation we have 80% chance who get relief from taking the medicine
b)

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

Mean ( np ) =16
Standard Deviation ( vnpq )= v20*0.8*0.2 = 1.7889

c)
The satandard deviation of the sampling sistribution