In analysis of variance, the assumption of normality, constant variance and independence are usually made, why?

The number of grams of fiber per serving for a random sample of three different kinds of foods is listed. Is there sufficient evidence at the 0.05 level of significance to conclude that there is a difference in mean fiber content among breakfast cereals, fruits, and vegetables? Breakfast...

The distribution for scores of a particular IQ test for adults is approximately normal with mean 100 and standard deviation 15. Given that the probability of IQ less than 106 is 0.6554, find the probability that at least 5 out of a randomly selected groups of 12 adults will have IQ less than 106.

A statisitics researcher collects data with a sample of 225 people indicating 170 of the perfer Nike athletic shoes over Asics athletic shoes. a. what is the 90% confidence interval for the proportion of people who prefer Nike ocer Asics? b. Which interpretation of that confidence intercal is...

I need help with these two 2nd year university statistics problem: Q.1 Let the discrete random variable of Y have a conditional uniform probability distribution on {1,2,. x}; ie: P(Y=y|X=x)=1/x, y=1,2,. x. Determine the unconditional mean and variance of Y in...