Statistics and Probability Answers

Let x₁,x₂,..., Xn be a random sample from N(μ,sigma²), where u is known. Construct a (1-a) * 100% Confidence Interval for sigma².

You are inclined to study on the problems encountered by 5 selected government colleges particularly on the performance of new teachers. The respondents of the study are the new teachers which relatively numbering for about 600. How would you choose the samples?

The latest nationwide political poll indicates that for Americans who are randomly selected, the probability that they are conservative is 0.55, the probability that they are liberal is 0.30, and the probability that they are middle – of –the road is 0.15. Assuming that theses probabilities are accurate, answer the following question pertaining to a randomly chosen group of 10 Americans.

A manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 64%. What is the probability that in a random sample of 480 headache sufferers, less than 59.1% obtain relief?

Draw the state transition rate diagram for the following queuing systems and from the diagram write down the equation of states: i) 𝑴/𝑴/𝟏(∞) queue with discouraged arrival rate, ii) 𝑴/𝑴/𝟏/𝑲: Finite Storage, iii) 𝑴/𝑴/𝒔/𝒔: s-Server Loss Systems, iv) 𝑴/𝑴/𝒔/𝑲/𝑴: Finite Population, s-Server Case, Finite Storage

Assume that random guesses are made for six multiple choice questions on an SAT​ test, so that there are n=6 ​trials, each with probability of success​ (correct) given by p=0.65. Find the indicated probability for the number of correct answers.

Find the probability that the number x of correct answers is fewer than 4.

If a fair coin is successively flipped, find the probability that a head first appears on the fifth trial.

using EXCEL.

Collect and Comment on the variability of three recent data sets describing similar processes (could be prices of three items over the last month, demographic information related to 3 countries over last year, etc.).

Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables following (1) binomial distribution [p,n], (2) a geometric distribution [p], and (3) Poisson

distribution [𝜆]. You have to consider two sets of parameters per distribution which can be chosen arbitrarily. The following steps can be followed:

1: Establish two sets of parameters of the distribution: For Geometric and Poisson distributions take two values of p (p1 and p2) and take two values of [𝜆], (𝜆1 and 𝜆2) respectively. For the binomial you should take two values of p and two values of n, first keep p fixed and change n, in the second keep n fixed and change p.