1. Find the mean, variance, standard deviation of the binomial distribution with the given values of n and p.
2. Use the contingency table to the right to calculate marginal frequencies and find the expected frequency for each cell in the contingency table. Assume that the variables are independent.
Result Brand name Generic Placebo
Improvement 18 28 16
No change 24 20 49
a)Calculate marginal frequencies and sample size.
b)Find the expected frequency for each cell in the contingency table.
3. Use the confidence interval to find the margin of error and sample mean.
Mean=np=122*.29=35.38 or 35.4
Variance=np(1-p)=122*.29*(1-.29)= 25.1198 or 25.1
Standard deviation=square roof of variance=25.1198^0.5=5.01197 or 5.0
There are three problems. Solution to first problem depicts the formulas to find mean, variance and standard deviation of a binomial distribution. Solution to second problem explains the methodology to calculate marginal frequencies and expected frequency for cell in the contingency table. Solution to third problem calculates the sample mean and margin of error.